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# In the system of equations to the right, z ≠ 0. What is ratio of x to

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Joined: 02 Sep 2009
Posts: 61549
In the system of equations to the right, z ≠ 0. What is ratio of x to  [#permalink]

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01 Jun 2017, 11:24
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35% (medium)

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71% (01:34) correct 29% (01:34) wrong based on 93 sessions

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In the system of equations to the right, z ≠ 0. What is ratio of x to z?

$$x + 2y − z = 1$$
$$3x − 2y − 8z = −1$$

(A) −9/4
(B) −1/3
(C) 1/3
(D) 4/9
(E) 9/4

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Re: In the system of equations to the right, z ≠ 0. What is ratio of x to  [#permalink]

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01 Jun 2017, 11:39
Top Contributor
Bunuel wrote:
In the system of equations to the right, z ≠ 0. What is ratio of x to z?

$$x + 2y − z = 1$$
$$3x − 2y − 8z = −1$$

(A) −9/4
(B) −1/3
(C) 1/3
(D) 4/9
(E) 9/4

Notice that the equations involve 3 variables (x, y and z), but the question asks about only 2 variables (x and z).
So, let's find a way to eliminate the y variable, so that we might be able to glean some information about the relationship between x and z.

Given:
x + 2y − z = 1
3x − 2y − 8z = −1

Add the two equations to get: 4x - 9z = 0
Add 9z to both sides to get: 4x = 9z

What is ratio of x to z?
So, we want the value of x/z
Take 4x = 9z
Divide both sides by z to get: 4x/z = 9
Divide both sides by 4 to get: x/z = 9/4

Cheers,
Brent
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Re: In the system of equations to the right, z ≠ 0. What is ratio of x to   [#permalink] 01 Jun 2017, 11:39
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