Question 1059785: 8x + 7y = –11
4x – 3y = 14
Answer by acw1213(28)   (Show Source):
You can put this solution on YOUR website! Solve this system using elimination.
First, look and see if you can easily multiply either equations to get a set of opposite or "same" coefficients.
4x is a factor of 8x, so you can multiply the second equation by 2.
2(4x - 3y = 14)
Your system should now look like:
8x + 7y = -11
8x - 6y = 28
The x's now have the same coefficients, so this means we need to subtract the equations.
The x's WILL CANCEL
7y - (-6y) = 7y + 6y = 13y
-11 - 28 = -39
Now, we are left with...
13y = -39
Solve for "y". Divide by 13 on both sides.
y = -3
Plug in -3 for "y" in either equation to solve for "x"
4x - 3(-3) = 14
Multiply -3 and -3 together.
4x + 9 = 14
Subtract by 9 on both sides
4x = 5
Divide by "4" on both sides.
x = 5/4
Your solution in (x,y) form is now (5/4,-3).
ALWAYS plug in your solution into your systems (ORIGINAL EQUATIONS!) to check your answer.
Plug in 5/4 for x, and -3 for y.
Does 8(5/4) + 7(-3) equal -11?
Let's check.
8*5/4 = 40/4 = 10
10 + 7(-3)
7*-3 = -21
10 + (-21)
10 - 21 = -11
YES! This solution works for this equation, but we still need to try the other!
Does 4(5/4) - 3(-3) equal 14?
Let's check!
4*5/4 = 20/4 = 5
5 - 3(-3)
-3*-3 = 9
5 + 9 = 14
YES! Our solution works for BOTH equations aka the SYSTEM. This is a CORRECT solution!
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