Posted by **Lexi** on Monday, November 22, 2010 at 11:13am.

For a test question, a mathematics teacher wants to find two constants a and b such that the test item "Simplify a(x + 2y) − b(2x − y)" will have an answer of -4x + 12y. What constants a and b should the teacher use?

- College Algebra -
**Reiny**, Monday, November 22, 2010 at 12:00pm
a(x + 2y) − b(2x − y) = -4x + 12y

ax + 2ay - 2bx + by = -4x + 12y

x(a-2b) + y(2a + b) = -4x + 12y

so a-2b = -4

and 2a + b = 12

first one times 2 ---> 2a - 4b = -8

second one ----> 2a + b = 12

subtract them: -5b = -20

b = 4

back in first: a - 8= - 4

a = 4

check:

4(x+2y) - 4(2x-y)

= 4x + 8y - 8x + 4y

= -4x + 12y , checks!

- College Algebra -
**Lexi**, Monday, November 22, 2010 at 3:44pm
awesome thanks!

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