Question

Solve the system of equations by substitution

$\left\{\begin{array}{l}2x-16y=8\\ -x-8y=-4\end{array}\right.$

Short answer

The solution for the system of equations is,

$$\begin{gathered} x=4 \\ y=0 \end{gathered}$$.

Step-by-step solution

Step 1. Given the information

The system of equations is,

$\left\{\begin{array}{l}2x-16y=8\\ -x-8y=-4\end{array}\right.$

Step 2. Finding the value of x from the first equation.

Using the equation $2x-16y=8$to find the value of $x$.

$2x-16y=8$

$2(x-8y)=8$

$x-8y=4$

$x=4+8y$

Step 3. Substituting the value of x in the equation.

Substituting $x=4+8y$in the equation

$-x-8y=-4$

$-(4+8y)-8y=-4$

$-4-8y-8y=-4$

$-16y-4=-4$

$-16y=-4+4$

$-16y=0$

$y=0÷(-16)$

$y=0$

Step 4. Substituting the value of y in the equation.

Substituting $y=0$in the equation

$x=4+8y$.

$x=4+8\left(0\right)$

$x=4+0$

$x=4$

Step 5. Checking the solution for the equation 2x-16y=8

Substituting $$\begin{gathered} x=4 \\ y=0 \end{gathered}$$in the equation

$2x-16y=8$

$2\left(4\right)-16\left(0\right)=8$

$8-0=8$

$8=8$

This is true.

Step 6. Checking the solution for the equation -x-8y=-4.

Substituting $$\begin{gathered} x=4 \\ y=0 \end{gathered}$$in the equation

$-x-8y=-4$

$-4-8\left(0\right)=-4$

$-4-0=-4$

$-4=-4$

This is true.