Question

Solve the system of equation$\left\{\begin{array}{l}y=x-6\\ y=-\frac{3}{2}x+6\end{array}\right.$by substitution

Short answer

The solution is$\left(4.8,-1.2\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$y=x-6\cdots \cdots \left(1\right)$

role="math" localid="1647790465247" $y=-\frac{3}{2}x+6\cdots \cdots \left(2\right)$

Step 2. Substitute value of y from equation 1 in equation 2

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

Step 3. Solve for x

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

$\Rightarrow \frac{5}{2}x=12$

$\Rightarrow 5x=24$

$\Rightarrow x=4.8$

Step 4. Substitute value of x from step 3 in equation 1

$\Rightarrow y=4.8-6$

$\Rightarrow y=-1.2$

Step 5. Checking solution  

Now we have $x=4.8$and$y=-1.2$

Put these values in equation $\left(1\right)$

$\Rightarrow -1.2=4.8-6$

$\Rightarrow -1.2=-1.2$

Also put these values in equation $\left(2\right)$

$\Rightarrow -1.2=-\frac{3}{2}\left(4.8\right)+6$

$\Rightarrow -1.2=-1.2$