College Algebra
posted by Lexi on .
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?

a(x + 2y) − b(2x − y) = 4x + 12y
ax + 2ay  2bx + by = 4x + 12y
x(a2b) + y(2a + b) = 4x + 12y
so a2b = 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(2xy)
= 4x + 8y  8x + 4y
= 4x + 12y , checks! 
awesome thanks!