Question

Solve the system:

$$\begin{gathered} -4\mathrm{x}+3\mathrm{y}=14 \\ \mathrm{y}=2\mathrm{x}+8 \end{gathered}$$

Answer 1

Step 1: Finding the value of $\mathrm{x}$.

Given:

$-4\mathrm{x}+3\mathrm{y}=14$ $........\left(1\right)$

$\mathrm{y}=2\mathrm{x}+8$ $........\left(2\right)$

Now put equation $2$ in equation $1$ we get,

$$\begin{gathered} -4\mathrm{x}+3(2\mathrm{x}+8)=14 \\ \Rightarrow -4\mathrm{x}+6\mathrm{x}+24=14 \\ \Rightarrow 2\mathrm{x}=14-24 \\ \Rightarrow 2\mathrm{x}=-10 \\ \Rightarrow \mathrm{x}=-5 \end{gathered}$$

Step 2: Finding the value of $\mathrm{y}$.

Put $\mathrm{x}=-5$ in $\mathrm{y}=2\mathrm{x}+8$ we get,

$$\begin{gathered} \mathrm{y}=2\times (-5)+8 \\ =-10+8 \\ =-2 \end{gathered}$$

Hence, we get $\mathrm{x}=-5$ and $\mathrm{y}=-2$.