Question

Solve the following system by elimination 2x-y=9 and 3x+4y=-14

Answer 1

2x - y = 9

3x + 4y = -14

To solve this system using elimination, one of the pairs of variable terms must cancel each other out. Their coefficients must be opposites of each other.

Multiply the top equation by 4.

2x - y = 9

4(2x - y = 9)

8x - 4y = 36

Add the equations together.

8x - 4y = 36

3x + 4y = -14

+___________

11x - 0 = 22

11x = 22

x = 2

Substitute 2 for x into either of the original equations to find y.

2x - y = 9

2(2) - y = 9

4 - y = 9

-y = 5

y = -5

Finally, check work by plugging x- and y-values into each original equation.

2(2) - (-5) = 9 --> 4 + 5 = 9 --> 9 = 9 --> True

3(2) + 4(-5) = -14 --> 6 - 20 = -14 --> -14 = -14 --> True

Answer:

x = 2 and y = -5; (2, -5).