Question

Solve the system of equations by substitution

$\left\{\begin{array}{l}2x+y=5\\ x-2y=-15\end{array}\right.$

Short answer

The solution for the system of equations is,

$$\begin{gathered} x=-1 \\ y=7 \end{gathered}$$.

Step-by-step solution

Step 1. Given the information

The system of equations is,

$\left\{\begin{array}{l}2x+y=5\\ x-2y=-15\end{array}\right.$

Step 2. Solve the first equation for y

Solving the equation $2x+y=5$for $y$

$2x+y=5$

$y=5-2x$

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

Substituting $y=5-2x$in the equation

$x-2y=-15$

$x-2(5-2x)=-15$

$x-10+4x=-15$

$5x-10=-15$

$5x=-15+10$

$5x=-5$

$x=-5÷5$

$x=-1$

Step 4. Substituting the value of x in the equation

Substituting $x=-1$in the equation

$y=5-2x$

$y=5-2(-1)$

$y=5+2$

$y=7$

Step 5. Checking the solution for the equation 2x+y=5.

Substituting $$\begin{gathered} x=-1 \\ y=7 \end{gathered}$$in the equation

$2x+y=5$

$2(-1)+7=5$

$-2+7=5$

$5=5$

This is true.

Step 6. Checking the solution for the equation x-2y=-15

Substituting $$\begin{gathered} x=-1 \\ y=7 \end{gathered}$$in the equation

$x-2y=-15$

$-1-2\left(7\right)=-15$

$-1-14=-15$

$-15=-15$

This is true.