Question

Solve each system by the method of addition or subtraction.

$x+3y=7$

$x+2y=4$

Short answer

The solution of given system of equations is x = –2, y = 3.

Step-by-step solution

Step 1. Description of step.

Subtract $x+2y=4$from $x+3y=7$and simplify.

$(x+3y)–(x+2y)=7–4$

$y=3$

Step 2. Description of step.

Substitute 3 for y into $x+3y=7$, to find the value of x.

$x+3\times 3=7$

$x+9=7$

Step 3. Description of step.

Subtract 9 from both the sides of the equation obtained in step 2 to find the value of x.

$x+9–9=7–9$

$x=–2‎$

Therefore, the solution of given system of equations is x = –2, y = 3.