$24-6 y=2 x$ $\newline$ $6(y-2)=3+x$ $\newline$ Consider the system of equations. If $(x, y)$ is the solution to the system, then what is the value of $y+x$ ?

Full solution

24-6 y=2 x

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6(y-2)=3+x

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Consider the system of equations. If

(x, y)

is the solution to the system, then what is the value of

y+x

Solve for x: Solve the first equation for x. $\newline$ We have $24 - 6y = 2x$ . To solve for x, we divide both sides by $2$ . $\newline$ $x = \frac{24 - 6y}{2}$ $\newline$ $x = 12 - 3y$
Substitute $x$ into second equation: Substitute the expression for $x$ into the second equation. $\newline$ The second equation is $6(y - 2) = 3 + x$ . We substitute $x$ with $12 - 3y$ . $\newline$ $6(y - 2) = 3 + (12 - 3y)$
Simplify and solve for y: Simplify and solve for y. $\newline$ Expanding the left side, we get: $\newline$ $6y - 12 = 3 + 12 - 3y$ $\newline$ Combining like terms, we get: $\newline$ $6y + 3y = 3 + 12 + 12$ $\newline$ $9y = 27$ $\newline$ Dividing both sides by $9$ , we get: $\newline$ $y = \frac{27}{9}$ $\newline$ $y = 3$
Substitute $y$ into $x$ expression: Substitute the value of $y$ into the expression for $x$ . $\newline$ We have $x = 12 - 3y$ . Now that we know $y = 3$ , we substitute it in. $\newline$ $x = 12 - 3(3)$ $\newline$ $x = 12 - 9$ $\newline$ $x = 3$
Find $y + x$ : Add the values of $x$ and $y$ to find $y + x$ . $y + x = 3 + 3$ $y + x = 6$