Question

Intersection of Two Lines

x+y=3
2x+y=5

Solve by the Elimination Method

Answer 1

1x + 1y = 3 ⇒ 2x + 2y = 6
2x + 1y = 5 ⇒ 2x + 1y = 5
y = 1
2x + 1 = 5
- 1 - 1
2x = 4
2 2
x = 2
(x, y) = (2, 1)

Answer 2

`x+y=3 \ \ \ |* (-1) \\ 2x+y=5 \\ \\ -x-y=-3 \\ \underline{2x+y=5 \ \ \ \ } \\ 2x-x=5-3 \\ x=2 \\ \\ x+y=3 \\ 2+y=3 \\ y=3-2 \\ y=1 \\ \\ \hbox{the point of intersection - } (x,y)=(2,1)`