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Founder  Joined: 18 Apr 2015
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x -y+z=0 2x +y + 3z = 0 In the system of equations above, i [#permalink]
Expert's post 00:00

Question Stats: 81% (00:55) correct 18% (00:28) wrong based on 37 sessions
$$x - y + z=0$$

$$2x +y + 3z = 0$$

In the system of equations above, if $$z \neq 0$$, then the ratio of x to z is

(A) $$- \frac{2}{1}$$

(B) $$- \frac{4}{3}$$

(C) $$- \frac{1}{2}$$

(D) $$\frac{3}{4}$$

(E) $$\frac{4}{3}$$
[Reveal] Spoiler: OA

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Manager Joined: 26 Jan 2018
Posts: 189
GRE 1: Q165 V156 Followers: 1

Kudos [?]: 134 , given: 3

Re: x -y+z=0 2x +y + 3z = 0 In the system of equations above, i [#permalink]
From the equations, x+z = y.

Replacing y in 2nd equation with this value and solving for x/z give -4/3. GRE Instructor Joined: 10 Apr 2015
Posts: 3841
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Kudos [?]: 4513  , given: 69

Re: x -y+z=0 2x +y + 3z = 0 In the system of equations above, i [#permalink]
2
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Expert's post
Carcass wrote:
$$x - y + z=0$$

$$2x +y + 3z = 0$$

In the system of equations above, if $$z \neq 0$$, then the ratio of x to z is

(A) $$- \frac{2}{1}$$

(B) $$- \frac{4}{3}$$

(C) $$- \frac{1}{2}$$

(D) $$\frac{3}{4}$$

(E) $$\frac{4}{3}$$

Since we want to find the ratio $$\frac{x}{z}$$, we should try to eliminate the variable y

GIVEN:
$$x - y + z=0$$
$$2x +y + 3z = 0$$

Add the two equations to get: $$3x+4z=0$$

Subtract 4z from both sides to get: $$3x=-4z$$

Divide both sides by 3 to get: $$x=-\frac{4z}{3}$$

Divide both sides by z to get: $$\frac{x}{z}=-\frac{4}{3}$$

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: x -y+z=0 2x +y + 3z = 0 In the system of equations above, i   [#permalink] 13 Jun 2019, 05:28
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