Answer:
Solution: x = -1; y = 2
Explanation:
Method to solve: Elimination:
Solving for x:
- We can begin by multiplying first equation by 2 and the second equation by 3.
This will allow us to eliminate y when adding the equations since -6y + 6y = 0:
Multiplying 2x - 3y = 8 by 2:
2(2x - 3y = -8)
4x - 6y = -16
Multiplying 9x + 2y = -5 by 3:
3(9x + 2y = -5)
27x + 6y = -15
Now we can add the two equations to eliminate y and solve for x:
4x - 6y = -16
+
27x + 6y = -15
----------------------------------------------------------------------------------------------------------(4x + 27x) + (-6y + 6y) = (-16 - 15)
(31x = -31) / 31
x = -1
Thus, x = -1.
Solving for y:
Now we can solve for y by plugging in -1 for x in the first equation (2x - 3y = -8):
2(-1) - 3y = -8
(-2 - 3y = -8) + 2
(-3y = -6) / -3
y = 2
Thus, y = 2.
Checking the validity of the answers:
Now we can check that our answers are correct by plugging in -1 for x and 2 for y in both equations and seeing if we get the same answer on both sides of the equation:
Checking -1 for x and 2 for y in 2x - 3y = -8:
2(-1) - 3(2) = -8
-2 - 6 = -8
-8 = -8
Checking -1 for x and 2 for y in 9x + 2y = -5:
9(-1) + 2(2) = -5
-9 + 4 = -5
-5 = -5
Thus, our answer are correct.