Linear Equations in Two Variables

1. $(-3,4)$

To find the $y$-value that corresponds to $x=3$, let's substitute this $x$-value in the equation.

$\begin{aligned} &y-4=-2(x+3) \\ &y-4=-2(-3+3) \\ &y-4=-2 \cdot 0 \\ &y-4=0 \\ &y=4 \end{aligned}$

Therefore $(-3,4)$ is a solution of the equation.

2. $(-8, 8)$

To find the $x$-value that corresponds to $y=8$, let's substitute this $y$-value in the equation.

$\begin{aligned} -4 x-y &=24 \\ -4 x-8 &=24 \\ -32 &=4 x \\ -8 &=x \end{aligned}$

Therefore $(-8, 8)$ is a solution of the equation.

3. $(-5, -8)$

To find the $y$-value that corresponds to $x = -5$, let's substitute this xxx-value in the equation.

$\begin{aligned} -3 x+7 y &=5 x+2 y \\ -3 \cdot(-5)+7 y &=5 \cdot(-5)+2 y \\ 15+7 y &=-25+2 y \\ 5 y &=-40 \\ y &=-8 \end{aligned}$

Therefore $(-5, -8)$ is a solution of the equation.

4. $(-6, 8)$

To find the $x$-value that corresponds to $y = 8$, let's substitute this yyy-value in the equation.

$\begin{aligned} 2 x+3 y &=12 \\ 2 x+3 \cdot 8 &=12 \\ 2 x+24 &=12 \\ 2 x &=-12 \\ x &=-6 \end{aligned}$

Therefore $(-6, 8)$ is a solution of the equation.