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3x+5y=52

2x+4y=38

$3$ . $3 x+5 y=52$ $\newline$ $2 x+4 y=38$

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Solve equations involving like terms

Full solution

Q.

3

.

3 x+5 y=52

\newline

2 x+4 y=38

Multiply by $-1.5$ : Multiply the second equation by a number that will allow us to eliminate one of the variables when we subtract one equation from the other. $\newline$ We can multiply the second equation by $-1.5$ to make the coefficients of $y$ in both equations opposites. $\newline$ $-1.5 \times (2x + 4y) = -1.5 \times 38$ $\newline$ This gives us $-3x - 6y = -57$ .
Add to eliminate y: Add the new equation from Step $1$ to the first equation to eliminate y. $\newline$ $(3x + 5y) + (-3x - 6y) = 52 + (-57)$ $\newline$ This simplifies to $-y = -5$ .
Solve for y: Solve for y. $\newline$ To isolate y, we divide both sides by \(-1＂). $\newline$ -y / \(-1 = $-5$ / $-1$ ＂) $\newline$ This gives us y = \(5＂).
Substitute and solve for $x$ : Substitute the value of $y$ back into one of the original equations to solve for $x$ . We can use the second equation: $2x + 4y = 38$ . Substitute $y = 5$ into the equation: $2x + 4(5) = 38$ . This simplifies to $2x + 20 = 38$ .
Final step: Solve for $x$ : Solve for $x$ . $\newline$ Subtract $20$ from both sides of the equation to isolate $2x$ . $\newline$ $2x + 20 - 20 = 38 - 20$ $\newline$ This simplifies to $2x = 18$ . $\newline$ Now, divide both sides by $2$ to solve for $x$ . $\newline$ $\frac{2x}{2} = \frac{18}{2}$ $\newline$ This gives us $x = 9$ .

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