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 – Creator of greenlighttestprep.com

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