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.