If $\mathbf{2 x}+\mathbf{1 0 y}=\mathbf{3}$ and $-\mathbf{5 x}-\mathbf{8 y}=\mathbf{7}$ are true equations, what would be the value of $\mathbf{7 x}+\mathbf{1 8 y}$ ? $\newline$ Answer:

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Algebra 2

Find trigonometric ratios using multiple identities

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Q. If

\mathbf{2 x}+\mathbf{1 0 y}=\mathbf{3}

and

-\mathbf{5 x}-\mathbf{8 y}=\mathbf{7}

are true equations, what would be the value of

\mathbf{7 x}+\mathbf{1 8 y}

\newline

Answer:

Equations Setup: We have two equations: $\newline$ $1$ ) $2x + 10y = 3$ $\newline$ $2$ ) $-5x - 8y = 7$ $\newline$ We want to find the value of $7x + 18y$ . To do this, we can use the method of linear combination to eliminate one of the variables and find the value of the other variable.
Eliminating Variable x: First, let's multiply the first equation by $5$ and the second equation by $2$ to make the coefficients of $x$ the same (but opposite in sign) so that we can eliminate $x$ by adding the equations together. $\newline$ $5(2x + 10y) = 5(3)$ $\newline$ $2(-5x - 8y) = 2(7)$
Solving for y: After multiplying, we get: $\newline$ $10x + 50y = 15$ $\newline$ $-10x - 16y = 14$ $\newline$ Now we can add these two equations together to eliminate $x$ .
Substitute $y$ into Equation: Adding the equations gives us: $\newline$ $(10x - 10x) + (50y - 16y) = 15 + 14$ $\newline$ $0x + 34y = 29$ $\newline$ Now we have a single equation with only one variable, $y$ .
Solving for x: To find the value of $y$ , we divide both sides of the equation by $34$ : $\frac{34y}{34} = \frac{29}{34}$ $y = \frac{29}{34}$
Substitute $x$ and $y$ : Now that we have the value of $y$ , we can substitute it back into one of the original equations to find the value of $x$ . Let's use the first equation: $\newline$ $2x + 10y = 3$ $\newline$ $2x + 10(29/34) = 3$
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \frac{290}{34} = 3$
$2x + \frac{145}{17} = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \left(\frac{290}{34}\right) = 3$
$2x + \left(\frac{145}{17}\right) = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \left(\frac{290}{34}\right) = 3$
$2x + \left(\frac{145}{17}\right) = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us:
$\frac{29}{34}$ $4$
$\frac{29}{34}$ $5$
$\frac{29}{34}$ $6$
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \left(\frac{290}{34}\right) = 3$
$2x + \left(\frac{145}{17}\right) = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us:
$\frac{29}{34}$ $4$
$\frac{29}{34}$ $5$
$\frac{29}{34}$ $6$ Now we divide both sides by $\frac{29}{34}$ $7$ to find the value of $\frac{29}{34}$ $2$ :
$\frac{29}{34}$ $9$
$2x + \left(\frac{290}{34}\right) = 3$ $0$
$2x + \left(\frac{290}{34}\right) = 3$ $1$
$2x + \left(\frac{290}{34}\right) = 3$ $2$
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \frac{290}{34} = 3$
$2x + \frac{145}{17} = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us:
$\frac{29}{34}$ $4$
$\frac{29}{34}$ $5$
$\frac{29}{34}$ $6$ Now we divide both sides by $\frac{29}{34}$ $7$ to find the value of $\frac{29}{34}$ $2$ :
$\frac{29}{34}$ $9$
$2x + \frac{290}{34} = 3$ $0$
$2x + \frac{290}{34} = 3$ $1$
$2x + \frac{290}{34} = 3$ $2$ We now have the values of $\frac{29}{34}$ $2$ and $2x + \frac{290}{34} = 3$ $4$ :
$2x + \frac{290}{34} = 3$ $2$
$2x + \frac{290}{34} = 3$ $6$
We can substitute these values into the expression $2x + \frac{290}{34} = 3$ $7$ to find its value.
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \left(\frac{290}{34}\right) = 3$
$2x + \left(\frac{145}{17}\right) = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us:
$\frac{29}{34}$ $4$
$\frac{29}{34}$ $5$
$\frac{29}{34}$ $6$ Now we divide both sides by $\frac{29}{34}$ $7$ to find the value of $\frac{29}{34}$ $2$ :
$\frac{29}{34}$ $9$
$2x + \left(\frac{290}{34}\right) = 3$ $0$
$2x + \left(\frac{290}{34}\right) = 3$ $1$
$2x + \left(\frac{290}{34}\right) = 3$ $2$ We now have the values of $\frac{29}{34}$ $2$ and $2x + \left(\frac{290}{34}\right) = 3$ $4$ :
$2x + \left(\frac{290}{34}\right) = 3$ $2$
$2x + \left(\frac{290}{34}\right) = 3$ $6$
We can substitute these values into the expression $2x + \left(\frac{290}{34}\right) = 3$ $7$ to find its value.Substituting the values of $\frac{29}{34}$ $2$ and $2x + \left(\frac{290}{34}\right) = 3$ $4$ into the expression gives us:
\(7x + $18$ y = $7$ \left(-\frac{ $47$ }{ $17$ }\right) + $18$ \left(\frac{ $29$ }{ $34$ }\right)
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ : $\newline$ $2x + \left(\frac{290}{34}\right) = 3$ $\newline$ $2x + \left(\frac{145}{17}\right) = 3$ $\newline$ Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ : $\newline$ $\frac{29}{34}$ $0$ $\newline$ Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us: $\newline$ $\frac{29}{34}$ $4$ $\newline$ $\frac{29}{34}$ $5$ $\newline$ $\frac{29}{34}$ $6$ Now we divide both sides by $\frac{29}{34}$ $7$ to find the value of $\frac{29}{34}$ $2$ : $\newline$ $\frac{29}{34}$ $9$ $\newline$ $2x + \left(\frac{290}{34}\right) = 3$ $0$ $\newline$ $2x + \left(\frac{290}{34}\right) = 3$ $1$ $\newline$ $2x + \left(\frac{290}{34}\right) = 3$ $2$ We now have the values of $\frac{29}{34}$ $2$ and $2x + \left(\frac{290}{34}\right) = 3$ $4$ : $\newline$ $2x + \left(\frac{290}{34}\right) = 3$ $2$ $\newline$ $2x + \left(\frac{290}{34}\right) = 3$ $6$ $\newline$ We can substitute these values into the expression $2x + \left(\frac{290}{34}\right) = 3$ $7$ to find its value.Substituting the values of $\frac{29}{34}$ $2$ and $2x + \left(\frac{290}{34}\right) = 3$ $4$ into the expression gives us: $\newline$ $2x + \left(\frac{145}{17}\right) = 3$ $0$ Now we simplify the expression: $\newline$ $2x + \left(\frac{145}{17}\right) = 3$ $1$ $\newline$ Since the denominators are not the same, we need to find a common denominator to combine the fractions.
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \frac{290}{34} = 3$
$2x + \frac{145}{17} = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us:
$\frac{29}{34}$ $4$
$\frac{29}{34}$ $5$
$\frac{29}{34}$ $6$ Now we divide both sides by $\frac{29}{34}$ $7$ to find the value of $\frac{29}{34}$ $2$ :
$\frac{29}{34}$ $9$
$2x + \frac{290}{34} = 3$ $0$
$2x + \frac{290}{34} = 3$ $1$
$2x + \frac{290}{34} = 3$ $2$ We now have the values of $\frac{29}{34}$ $2$ and $2x + \frac{290}{34} = 3$ $4$ :
$2x + \frac{290}{34} = 3$ $2$
$2x + \frac{290}{34} = 3$ $6$
We can substitute these values into the expression $2x + \frac{290}{34} = 3$ $7$ to find its value.Substituting the values of $\frac{29}{34}$ $2$ and $2x + \frac{290}{34} = 3$ $4$ into the expression gives us:
$2x + \frac{145}{17} = 3$ $0$ Now we simplify the expression:
$2x + \frac{145}{17} = 3$ $1$
Since the denominators are not the same, we need to find a common denominator to combine the fractions.The common denominator for $17$ and $2x + \frac{145}{17} = 3$ $3$ is $2x + \frac{145}{17} = 3$ $3$ . We multiply the first fraction by $2x + \frac{145}{17} = 3$ $5$ to get the same denominator:
$2x + \frac{145}{17} = 3$ $6$
Now we can combine the fractions.
Combine and Simplify Fractions: Simplify the equation by multiplying $10$ with $\frac{29}{34}$ :
$2x + \left(\frac{290}{34}\right) = 3$
$2x + \left(\frac{145}{17}\right) = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us:
$\frac{29}{34}$ $4$
$\frac{29}{34}$ $5$
$\frac{29}{34}$ $6$ Now we divide both sides by $\frac{29}{34}$ $7$ to find the value of $\frac{29}{34}$ $2$ :
$\frac{29}{34}$ $9$
$2x + \left(\frac{290}{34}\right) = 3$ $0$
$2x + \left(\frac{290}{34}\right) = 3$ $1$
$2x + \left(\frac{290}{34}\right) = 3$ $2$ We now have the values of $\frac{29}{34}$ $2$ and $2x + \left(\frac{290}{34}\right) = 3$ $4$ :
$2x + \left(\frac{290}{34}\right) = 3$ $2$
$2x + \left(\frac{290}{34}\right) = 3$ $6$
We can substitute these values into the expression $2x + \left(\frac{290}{34}\right) = 3$ $7$ to find its value.Substituting the values of $\frac{29}{34}$ $2$ and $2x + \left(\frac{290}{34}\right) = 3$ $4$ into the expression gives us:
$2x + \left(\frac{145}{17}\right) = 3$ $0$ Now we simplify the expression:
$2x + \left(\frac{145}{17}\right) = 3$ $1$
Since the denominators are not the same, we need to find a common denominator to combine the fractions.The common denominator for $17$ and $2x + \left(\frac{145}{17}\right) = 3$ $3$ is $2x + \left(\frac{145}{17}\right) = 3$ $3$ . We multiply the first fraction by $2x + \left(\frac{145}{17}\right) = 3$ $5$ to get the same denominator:
$2x + \left(\frac{145}{17}\right) = 3$ $6$
Now we can combine the fractions.Combining the fractions gives us:
$2x + \left(\frac{145}{17}\right) = 3$ $7$
\left(\frac{$-658$ + $522$}{$34$}\right) = \left(\frac{$-136$}{$34$}\right)
Combine and Simplify Fractions: Simplify the equation by multiplying \(10 with $\frac{29}{34}$ :
$2x + \frac{290}{34} = 3$
$2x + \frac{145}{17} = 3$
Now we need to convert $3$ to a fraction with a denominator of $17$ to combine it with $\frac{145}{17}$ .Converting $3$ to a fraction with a denominator of $17$ gives us $\frac{51}{17}$ :
$\frac{29}{34}$ $0$
Now we can subtract $\frac{145}{17}$ from both sides to solve for $\frac{29}{34}$ $2$ .Subtracting $\frac{145}{17}$ from both sides gives us:
$\frac{29}{34}$ $4$
$\frac{29}{34}$ $5$
$\frac{29}{34}$ $6$ Now we divide both sides by $\frac{29}{34}$ $7$ to find the value of $\frac{29}{34}$ $2$ :
$\frac{29}{34}$ $9$
$2x + \frac{290}{34} = 3$ $0$
$2x + \frac{290}{34} = 3$ $1$
$2x + \frac{290}{34} = 3$ $2$ We now have the values of $\frac{29}{34}$ $2$ and $2x + \frac{290}{34} = 3$ $4$ :
$2x + \frac{290}{34} = 3$ $2$
$2x + \frac{290}{34} = 3$ $6$
We can substitute these values into the expression $2x + \frac{290}{34} = 3$ $7$ to find its value.Substituting the values of $\frac{29}{34}$ $2$ and $2x + \frac{290}{34} = 3$ $4$ into the expression gives us:
$2x + \frac{145}{17} = 3$ $0$ Now we simplify the expression:
$2x + \frac{145}{17} = 3$ $1$
Since the denominators are not the same, we need to find a common denominator to combine the fractions.The common denominator for $17$ and $2x + \frac{145}{17} = 3$ $3$ is $2x + \frac{145}{17} = 3$ $3$ . We multiply the first fraction by $2x + \frac{145}{17} = 3$ $5$ to get the same denominator:
$2x + \frac{145}{17} = 3$ $6$
Now we can combine the fractions.Combining the fractions gives us:
$2x + \frac{145}{17} = 3$ $7$
$2x + \frac{145}{17} = 3$ $8$ Finally, we simplify the fraction by dividing both the numerator and the denominator by $\frac{29}{34}$ $7$ :
$3$ $0$
So, the value of $2x + \frac{290}{34} = 3$ $7$ is $3$ $2$ .

If 2x+10y=3 \mathbf{2 x}+\mathbf{1 0 y}=\mathbf{3} 2x+10y=3 and −5x−8y=7 -\mathbf{5 x}-\mathbf{8 y}=\mathbf{7} −5x−8y=7 are true equations, what would be the value of 7x+18y \mathbf{7 x}+\mathbf{1 8 y} 7x+18y ?\newlineAnswer:

If $\mathbf{2 x}+\mathbf{1 0 y}=\mathbf{3}$ and $-\mathbf{5 x}-\mathbf{8 y}=\mathbf{7}$ are true equations, what would be the value of $\mathbf{7 x}+\mathbf{1 8 y}$ ? $\newline$ Answer: