solve using the elimination method. -2x-8y=-42, -4x+6y=-18

Question

if the system has no solution or an infinite number of solutions, state this

Answer 1

Elimination method

Given equation -2x-8y = -42

Multiple to each side by negitive 2.

4x+16y = 84 ----------> (1)

And -4x+6y = -18 ----------> (2)

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

4x+16y = 84

-4x+6y = -18

__________

22y = 66

Divide to each side by 22.

22y/22 = 66/22

⇒ y = 3

Substitue the y value in (1).

4x+16*3 = 84

4x+48 = 84

 subtract 48 to each side.

4x+48-48 = 84-48

4x = 36

Divide to each side by 4.

4x/4 = 36/4

⇒ x = 9

Solutin x =9, y = 3.