Question

Solve the system:

$$\begin{gathered} \mathrm{x}+\mathrm{y}=-4 \\ 6\mathrm{x}+2\mathrm{y}=4 \end{gathered}$$

Answer 1

Step 1: Multiplying equation $1$ with $\text{'}2\text{'}$.

Given:

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

$6\mathrm{x}+2\mathrm{y}=4$ $........\left(2\right)$

Multiplying equation $1$ with $\text{'}2\text{'}$we get,

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

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

Now subtract equation $\left(3\right)$ from $\left(2\right)$

$6\mathrm{x}+2\mathrm{y}=4-2\mathrm{x}+2\mathrm{y}=-84\mathrm{x}+0\mathrm{y}=12$

We get,

$$\begin{gathered} 4\mathrm{x}=12 \\ \Rightarrow \mathrm{x}=3 \end{gathered}$$

Step 3: Finding the value of $\mathrm{y}$.

Put $\mathrm{x}=3$ in $\mathrm{x}+\mathrm{y}=-4$ we get,

$$\begin{gathered} 3+\mathrm{y}=-4 \\ \Rightarrow \mathrm{y}=-4-3 \\ \Rightarrow \mathrm{y}=-7 \end{gathered}$$

Therefore, we get $\mathrm{x}=3$ and $\mathrm{y}=-7$.