Question

Solve the system of equations by substitution

$\left\{\begin{array}{l}y=x-6\\ y=-\frac{3}{2}x+4\end{array}\right.$

Short answer

The solution for the system of equations is

$$\begin{gathered} x=4 \\ y=-2 \end{gathered}$$.

Step-by-step solution

Step 1. Given the information

The system of equations is,

$\left\{\begin{array}{l}y=x-6\\ y=-\frac{3}{2}x+4\end{array}\right.$

Step 2. Substituting the value of y in the equation.

Substituting $y=x-6$in the equation

$y=-\frac{3}{2}x+4$

$x-6=-\frac{3}{2}x+4$

$x+\frac{3}{2}x=4+6$

$\frac{2x+3x}{2}=10$

$\frac{5}{2}x=10$

$x=10÷\frac{5}{2}$

$x=10\times \frac{2}{5}$

$x=4$

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

Substituting $x=4$in the equation

$y=x-6$

$y=4-6$

$y=-2$

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

Substituting $$\begin{gathered} x=4 \\ y=-2 \end{gathered}$$in the equation

$y=x-6$

$-2=4-6$

$-2=-2$

This is true.

Step 5. Checking the solution for the equation y=-32x+4

Substituting $$\begin{gathered} x=4 \\ y=-2 \end{gathered}$$in the equation

$y=-\frac{3}{2}x+4$

$-2=-\frac{3}{2}\left(4\right)+4$

$-2=-6+4$

$-2=-2$

This is true.