Quick Math Question: Ratios/System of Equations

Test Preparation
1

<p>Multiple choice question #30 from the GRE 10th edition practice book page 212:</p>

<p>x - y + z = 0
2x + y + 3z = 0</p>

<p>"In the system of equations above, if z does not equal 0, then the ratio of x to z is?"</p>

<p>A) -(2/1)
B) -(4/3)
C) -(1/2)
D) (3/4)
E) (4/3)</p>

<p>I correctly got the answer -(4/3), but I really don't understand why it is the right answer. I eliminated the y variable by solving for y in the first equation (y = x + z) and then substituting for y in the second equation. I then solved for x to get -(4/3).</p>

<p>Am I using the right process and just got the right answer because it just so happened to work out? When solving the problem, I got caught up in the whole system of equations and solving for x that I forgot the question was asking me for a ratio and I thought it was asking me to solve for x. When I go back to find a ratio, I get the equation 3x = -4z (which is the step before getting x = (-4/3)z ). Shouldn't the answer then be -(3/4).</p>

<p>What am I missing??</p>

2

<p>First thing your missing is the logic behind the question. </p>

<p>Two equations three unknowns you can’t solve the equation so don’t waste your time. Your looking for a ratio not what x or y or z is. </p>

<p>Step 1 Don’t do more work then you have to. Add the equations together. </p>

<p>3x+4z=0</p>

<p>Step 2 Rearrange
3x=-4z</p>

<p>Step 3 (Read the question) ratio of x to z means x:z or x/z thus
x:z= -4/3</p>

3

<p>If 3x = -4z, why is the ratio of x:z -4/3 and not 3/-4?</p>

4

<p>3x=-4z divide both sides by z
.
3x/z=-4 divide both sides by 3
.
x/z=-4/3
.
x/z=ratio of x to z=-4/3
.
The important thing is the translation of “ratio of x to z”. This means x divided by z. As the equation shows, x/z=-4/3, but z/x=3/-4</p>

5

<p>Ohhh thank you!</p>

6

<p>No problem. Any other questions? :)</p>