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# 4x + y + 3z = 34 4x + 3z = 21 What is the value of y?

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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4x + y + 3z = 34 4x + 3z = 21 What is the value of y? [#permalink]  23 Jun 2018, 11:47
Expert's post
00:00

Question Stats:

100% (00:14) correct 0% (00:00) wrong based on 10 sessions
$$4x + y + 3z = 34$$
$$4x + 3z = 21$$

What is the value of y?

[Reveal] Spoiler: OA
13

_________________

Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: 4x + y + 3z = 34 4x + 3z = 21 What is the value of y? [#permalink]  16 Jul 2018, 18:55
Expert's post
Explanation

This question contains only two equations, but three variables. To isolate y, both x and z must be eliminated. Notice that the coefficients of x and z are the same in both equations. Subtract the second equation from the first to eliminate x and z.

$$4x + y + 3z = 34$$
$$-(4x + 3z = 21)$$
$$y = 13$$
_________________

Sandy
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Joined: 09 Jul 2018
Posts: 10
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Kudos [?]: 7 [1] , given: 0

Re: 4x + y + 3z = 34 4x + 3z = 21 What is the value of y? [#permalink]  18 Jul 2018, 17:57
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KUDOS
sandy wrote:
$$4x + y + 3z = 34$$
$$4x + 3z = 21$$

What is the value of y?

[Reveal] Spoiler: OA
13

This is super simple if you look at the equations closely and rearange them to look like this:
$$4x + 3z + y = 34$$
$$4x + 3z = 21$$

Notice how $$4x + 3z$$ already equals 21? Well plug that in:
$$21 + y = 34$$
$$y = 13$$

The answer is $$y = 13$$
Re: 4x + y + 3z = 34 4x + 3z = 21 What is the value of y?   [#permalink] 18 Jul 2018, 17:57
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# 4x + y + 3z = 34 4x + 3z = 21 What is the value of y?

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