Question

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

$$\begin{gathered} 15x+2y=6 \\ -5x+2y=-4 \end{gathered}$$

Short answer

The ordered pair is$(\frac{1}{2},-\frac{3}{4})$

Step-by-step solution

Step 1. Given Information

The given equations are

$$\begin{gathered} 15x+2y=6 \\ -5x+2y=-4 \end{gathered}$$

Step 2. Calculation

Solve the given equation for variable y.

$$\begin{gathered} 15x+2y=6 \\ 2y=6-15x \\ y=\frac{6-15x}{2} \end{gathered}$$

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

$$\begin{gathered} -5x+2(3-\frac{15}{2}x)=-4 \\ -5x+6-15x=-4 \\ -20x=-10 \\ x=\frac{1}{2} \end{gathered}$$

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

$$\begin{gathered} y=3-\frac{15}{2}\left(\frac{1}{2}\right) \\ y=3-\frac{15}{4} \\ y=\frac{12-15}{4} \\ y=-\frac{3}{4} \end{gathered}$$