Carcass wrote:
Solve each of the following systems of equations for x and y.
(a) \(x+y=24\) ; \(x − y=18\)
(b) \(3x−y=−5 ; x+2y=3\)
(c) \(15x−18−2y=−3x+y ; 10x+7y+20=4x+2\)
(a) x = 21 , y = 3 (b) x =− 1, y = 2 (c) \(x=\frac{1}{2}\) , y=-3
Math Review
Question: 7
Page: 244
Difficulty: medium
(a)
\(x+y=24\)
\(x−y=18\)
ADD the equations to get: \(2x=42\)
Solve: \(x=21\)
Take \(x+y=24\)
Replace x with 21 to get: \(21+y=24\)
Solve: \(y=3\)
Solution: \(x=21\) and \(y=3\)
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(b)
\(3x−y=−5\)
\(x+2y=3\)
Take top equation and multiply both sides by 2 to get:
\(6x−2y=−10\)
\(x+2y=3\)
ADD the two equations to get:
\(7x=-7\)
Solve: \(x=-1\)
Take \(3x−y=−5\)
Replace x with -1 to get: \(3(-1)−y=−5\)
Expand to get: \(-3-y=−5\)
Solve to get: y = 2
Solution: \(x=-1\) and \(y=2\)
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(c)
\(15x−18−2y=−3x+y\)
\(10x+7y+20=4x+2\)
Simplify each equation to get:
\(18x−3y=18\)
\(6x+7y=-18\)
Take bottom equation and multiply both sides by 3 to get:
\(18x−3y=18\)
\(18x+21y=-54\)
SUBTRACT the bottom equation from the top equation to get:
\(-24y = 72\)
Solve: \(y = -3\)
Take \(18x−3y=18\)
Replace y with -3 to get: \(18x−3(-3)=18\)
Simplify to get: \(18x+9=18\)
Subtract 9 from both sides to get: \(18x=9\)
Solve to get: \(x=\frac{9}{18}=\frac{1}{2}\)
Solution: \(x=\frac{1}{2}\) and \(y=-3\)
Cheers,
Brent
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Brent Hanneson - founder of Greenlight Test Prep