Question

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

Short answer

The solution is$\left(6,6\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$3x-2y=6\cdots \cdots \left(1\right)$

$y=\frac{2}{3}x+2\cdots \cdots \left(2\right)$

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

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

Step 3. Solve for x

$\Rightarrow 3x-\frac{4}{3}x-4=6$

$\Rightarrow \frac{9x-4x}{3}=6+4$

$\Rightarrow \frac{5}{3}x=10$

$\Rightarrow 5x=30$

$\Rightarrow x=6$

Step 4. Substitute value of x from step 3 in equation 2

$\Rightarrow y=\frac{2}{3}\left(6\right)+2$

$\Rightarrow y=4+2$

$\Rightarrow y=6$

Step 5. Checking solution 

Now we have $x=6$and$y=6$

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

$\Rightarrow 3\left(6\right)-2\left(6\right)=6$

$\Rightarrow 6=6$

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

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

$\Rightarrow 6=6$