Question

Solve $8\mathrm{x}+2\mathrm{y}=-12,5\mathrm{x}-\mathrm{y}=4$

Answer 1

Find out the value for $\mathrm{x}\mathrm{and}\mathrm{y}$:

Here the two equations are ;

$$\begin{gathered} 8\mathrm{x}+2\mathrm{y}=-12...\left(1\right) \\ 5\mathrm{x}-\mathrm{y}=4...\left(2\right) \end{gathered}$$

To solve, Multiply $\left(2\right)\mathrm{by}2$ :

$10\mathrm{x}-2\mathrm{y}=8...\left(3\right)$

To eliminate $y$ , add both the equation $\left(1\right)\mathrm{and}\left(3\right)$:

$$\begin{gathered} 8x+2y+10\mathrm{x}-2\mathrm{y}=-12+8 \\ \Rightarrow 18\mathrm{x}=-4 \\ \Rightarrow \mathrm{x}=\frac{-4}{18}\left[\mathrm{divide}18\mathrm{from}\mathrm{both}\mathrm{side}\right] \\ \Rightarrow \mathrm{x}=\frac{-2}{9} \end{gathered}$$

To get $y$, substitute $x=\frac{-2}{9}$ in the equation $\left(2\right)$:

$$\begin{gathered} 5\times \frac{-2}{9}-\mathrm{y}=4 \\ \Rightarrow \mathrm{y}=-4-\frac{10}{9} \\ \Rightarrow \mathrm{y}=\frac{-46}{9} \end{gathered}$$

Hence, the required value are $\mathrm{x}=\frac{-2}{9}\mathrm{and}\mathrm{y}=\frac{-46}{9}.$