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).
