Question

In the following exercises, solve the systems of equations by substitution.

$\left\{\begin{array}{l}x-y=0\\ 2x+5y=-14\end{array}\right.$

Short answer

The solution for the system of linear equations is$\left(-2,-2\right)$.

Step-by-step solution

Step 1. Given information. 

The system of linear equations,

$\left\{\begin{array}{l}x-y=0\\ 2x+5y=-14\end{array}\right.$

Step 2. Substituting the value of y from one equation into another equation. 

$$\begin{gathered} x-y=0 \\ y=x \end{gathered}$$

Now substituting this in another equation we get

$$\begin{gathered} 2x+5x=-14 \\ 7x=-14 \\ x=-2 \end{gathered}$$

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

$$\begin{gathered} 2\left(-2\right)+5y=-14 \\ -4+5y=-14 \\ 5y=-10 \\ y=-2 \end{gathered}$$

Step 4. Checking the result.

Substituting the value of $x$and $y$in the first equation then

$$\begin{gathered} x-y=0 \\ -2-(-2)=0 \\ -2+2=0 \\ 0=0 \end{gathered}$$

Substituting the value of $x$and $y$in the second equation then

$$\begin{gathered} 2x+5y=-14 \\ 2(-2)+5(-2)=-14 \\ -4-10=-14 \\ -14=-14 \end{gathered}$$

Hence, this is true.