Question

Solve the system of equation$\left\{\begin{array}{l}y=2x-8\\ y=\frac{3}{5}x+6\end{array}\right.$by substitution

Short answer

The solution is$\left(10,12\right)$.

Step-by-step solution

Step 1. Given information 

The given equations are:

$y=2x-8\cdots \cdots \left(1\right)$

$y=\frac{3}{5}x+6\cdots \cdots \left(2\right)$

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

$\Rightarrow 2x-8=\frac{3}{5}x+6$

Step 3. Solve for x

$\Rightarrow 2x-\frac{3}{5}x=6+8$

localid="1649176532530" $\Rightarrow \frac{7}{5}x=14$

localid="1649176558563" $\Rightarrow 7x=70$

localid="1649176568889" $\Rightarrow x=10$

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

$\Rightarrow y=2\left(10\right)-8$

$\Rightarrow y=20-8$

$\Rightarrow y=12$

Step 5. Checking solution  

Now we have $x=10$and$y=12$

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

localid="1649176636088" $\Rightarrow 12=2\left(10\right)-8$

localid="1649176644646" $\Rightarrow 12=12$

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

localid="1649176731054" $\Rightarrow 12=\frac{3}{5}\left(10\right)+6$

$\Rightarrow 12=12$