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What is the answer to 4x plus 8y equals 20 and -4x plus 2y equals -30 by solving using elimination?
- 4x + 8y = 20
- -4x + 2y = -30
- First add equations 1. & 2. to get:
(4x + -4x) + (8y + 2y) = 20 + -30
⇒ 10y = -10
⇒ y = -1
- Multiply equation 2. by 4 and subtract it from equation 1:
- 4x + 8y = 20
- -16x + 8y = -120
⇒ (4x - -16x) + (8y - 8y) = 20 - -120
⇒ 20x = 140
⇒ x = 7
Solution x = 7, y = -1
Alternatively, to find x, now that y is known to be -1:
Substitute y = -1 into equation 1. to give:
4x + 8(-1) = 20
⇒ 4x -8 = 20
⇒ 4x = 28
⇒ x = 7
The solution can be checked y substituting the values found for x and y in to equation 2. and checking it is the correct value:
-4x + 2y = -4(7) + 2(-1)
= -28 + -2
= -30
as required, so the solution is correct.
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