Question

Solve the system of equation$\left\{\begin{array}{l}-x-12y=-1\\ 2x-8y=-6\end{array}\right.$by substitution

Short answer

The solution is$\left(-2,0.25\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$-x-12y=-1\cdots \cdots \left(1\right)$

$2x-8y=-6\cdots \cdots \left(2\right)$

Step 2. Substitute value of x from equation 1 in equation 2

From equation $\left(1\right)$$x=1-12y$

Substitute in equation $\left(2\right)$

localid="1649347861698" $\Rightarrow 2\left(1-12y\right)-8y=-6$

Step 3. Solve for y

$\Rightarrow 2-24y-8y=-6$

$\Rightarrow -32y=-8$

$\Rightarrow y=\frac{8}{32}$

$\Rightarrow 0.25$

Step 4. Substitute value of y from step 3 in equation 1

$\Rightarrow -x-12\left(0.25\right)=-1$

$\Rightarrow -x-3=-1$

$\Rightarrow x=1-3$

$\Rightarrow x=-2$

Step 5. Checking solution

As we know $x=-2$and $y=0.25$

Put these values in equation $\left(1\right)$

localid="1649348056337" $\Rightarrow -\left(-2\right)-12\left(0.25\right)=-1$

$\Rightarrow -1=-1$

Als put these values in equation $\left(2\right)$

localid="1649348080137" $\Rightarrow 2\left(-2\right)-8\left(0.25\right)=-6$

localid="1649348095034" $\Rightarrow -6=-6$