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Solve each of the following systems of equations for x and y [#permalink]
Expert's post
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) $$15x−18−2y=−3x+y ; 10x+7y+20=4x+2$$

[Reveal] Spoiler: OA
(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

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GRE Instructor Joined: 10 Apr 2015
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Re: Solve each of the following systems of equations for x and y [#permalink]
Expert's post
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) $$15x−18−2y=−3x+y ; 10x+7y+20=4x+2$$

[Reveal] Spoiler: OA
(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 $$y=3$$
------------------------------

(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 $$y=2$$
---------------------------

(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
If you enjoy my solutions, you'll like my GRE prep course.  Re: Solve each of the following systems of equations for x and y   [#permalink] 24 May 2019, 13:18
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