Question

Solve each system by the method of addition or subtraction.

$5x–y=20$

$3x+y=12$

Short answer

The solution of given system of equations is x = 4, y = 0.

Step-by-step solution

Step 1. Description of step.

Add $5x-y=20$and $3x+y=12$and simplify.

$(5x–y)+(3x+y)=20+12$

$8x=32$

Step 2. Description of step.

Divide each side of the equation obtained in step 1 by 8 to find the value of x.

$\frac{8x}{8}=\frac{32}{8}$

$x=4$

Step 3. Description of step.

Substitute 4 for x into $3x+y=12$, to find the value of y.

$3\times 4+y=12$

$12+y=12$

$y=0$

Therefore, the solution of given system of equations is x = 4, y = 0.