Question

Solve each system by the method of addition or subtraction.

$7x+y=29$

$5x+y=21$

Short answer

The solution of given system of equations is x = 4, y = 1.

Step-by-step solution

Step 1. Description of step.

Subtract $5x+y=21$from $7x+y=29$and simplify.

$(7x+y)–(5x+y)=29–21$

$2x=8$

Step 2. Description of step.

Divide each side of the equation obtained in step 1 by 2 to find the value of x.

$\frac{2x}{2}=\frac{8}{2}$

$x=4$

Step 3. Description of step.

Substitute for x into $5x+y=21$, to find the value of y.

$5\times 4+y=21$

$20+y=21$

$y=1$

Therefore, the solution of given system of equations is x = 4, y = 1.