### Home > PC3 > Chapter 2 > Lesson 2.2.1 > Problem2-51

2-51.

​Algebraically solve each system of equations and state the method you used. Graphically check your answers.

1. $y=2x+1$
$2x-2y=-11$

Use substitution.

$2x-2(2x+1)=-11$

1. $\frac{1}{3}x+\frac{2}{3}y=5$
$5x-2y=15$

Multiply the top equation by $15$.

$15\Big(\frac{1}{3}x+\frac{2}{3}y\Big)=15(5)$

$5x+10y=75$

Subtract the bottom equation from the new top equation.

$12y=60$