how do you solve -x + 2y= 1 and x+ y=5

Question

solve the linear system by addition-elimation method. (FInd the intersection of the two lines).

Answer 1

Elimination method

Given equations are -x +2y  = 1 ---> (1)

x +y  = 5 ---> (2)

To eliminate the x  value add the equations (1)&(2).

-x +2y  = 1

x +y  = 5

______________

3y  = 6

Divide to each side by 3.

y  = 2

Substitute the x  value in (2).

x +2 = 5

Subtract 2 from each side.

x  = 3

Solution x = 3, y  = 2.

Intersection point of two lines is (3,2).