Question

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

$$\begin{gathered} 2x-15y=7 \\ 12x+2y=-4 \end{gathered}$$

Short answer

The ordered pair is$(\frac{-1}{4},\frac{-1}{2})$

Step-by-step solution

Step 1. Given Information 

The given equations are

$$\begin{gathered} 2x-15y=7 \\ 12x+2y=-4 \end{gathered}$$

Step 2. Calculation

Solve the second equation for variable y.

$$\begin{gathered} 12x+2y=-4 \\ 2y=-4-12x \\ y=\frac{-4-12x}{2} \\ y=-2-6x \end{gathered}$$

Now substitute the obtained value of y in the first equation, we get,

$$\begin{gathered} 2x-15(-2-6x)=7 \\ 2x+30+90x=7 \\ 92x=-23 \\ x=\frac{-1}{4} \end{gathered}$$

Substitute the value of x to find the value of variable y.

$$\begin{gathered} y=-2-6\left(\frac{-1}{4}\right) \\ y=-2+\frac{3}{2} \\ y=\frac{-4+3}{2} \\ y=-\frac{1}{2} \end{gathered}$$