algebra 1 homework help

Question

find the intersection of the 2 lines of this equation?

2x+3y=13 and 6x-2y=-5

Answer 1

The solution set can be found by solving the problem using elimination method

2x+3y=13 multiply the equation by 2.

4x + 6y = 26 ------------ (1)

6x-2y=-5 multiply the equation by 3.

18x - 6y = -15 ---------- (2)

Add equations 1 and 2.

4x + 6y = 26
18x - 6y = -15
---------------
22x = 11

Divide each side by 22.

x = 11/22 = 1/2

substitute x = 1/2 in 2x+3y=13.

2 * 1/2 + 3y = 13

3y = 13 -1 =12

Divide each side by 4.

y = 4

(x, y) = (1/2, 4).