Question

Given equasions A and B as 2/5x + 3/5y = 12 and 5/2y - 3x = 6, respectively, which expression will eliminate the variable y?
A. 5/3A + 2/5B
B. 5/3A - B
C. A - 2/5B
D. 5/3A - 2/5B
E. 25/15A + 6/15B

Answer 1

Look at your equations and hunt for a pair of coefficients that are opposite in sign and can be made equal in magnitude by multiplying one of them by some number. Here they've thrown you a curve ball by writing the equations in different order hoping to get you to say "oh, I just multiply A by 3" :-) Easier to see what to do if they are in the same order:
\[A: \frac{2}{5}x+\frac{3}{5}y = 12\]\[B: -3x + \frac{5}{2}y = 6\]

Answer 2

I see upon rereading that they've already decided you are to eliminate \(y\). In that case, ignore the part about looking for opposite signs, you're going to make that be true by your multiplication.

Answer 3

Thanks:) makes it a lot simpler. Wouldn't the answer be A or B?

Answer 4

Well, let's look:

A: 5/3A + 2/5B

if we multiply A by 5/3, we get
\[\frac{5}{3}*\frac{2}{5}x + \frac{5}{3}*\frac{3}{5}y = \frac{5}{3}12\]\[\frac{2}{3}x + y = 20\]

if we multiply B by 2/5, we get
\[\frac{2}{5}*-3x + \frac{2}{5}*\frac{5}{2}y = \frac{2}{5}6\]\[-\frac{6}5 x+ y = \frac{12}5\]
y term won't be eliminated

Answer 5

for B: 5/3A - B
using our previous results,
5/3A = 2x/3 + y = 20
-B = -(-3x) -5y/2 = -6

y won't be eliminated there either

Answer 6

Can you find another choice that is like A (which gets us equal coefficients in \(y\) but not the right signs)?

Answer 7

are there any that have -2/5 B instead of +2/5 B?