For a test question, a mathematics teacher wants to find two constants a and b such that the test item "Simplify a(-9x + 2y) - b(7x - 4y) " will have an answer of (46x - 20y). What constants should the teacher use for a and b?
I have no idea where to start.
2007-11-16 11:04:42 · 5 answers · asked by thebodyelectric! 1 in Science & Mathematics ➔ Mathematics
wow you explained that better than my teacher did. thanks!
2007-11-16 11:27:18 · update #1
a(-9x + 2y) - b(7x - 4y) = (46x - 20y)
-9a x + 2a y - 7b x + 4b y = 46x - 20y
x (-9a-7b) + y (2a+4b) = 46 x - 20 y
-9a - 7b = 46
2a+4b = -20
Solve these equations to find a and b.
Bye!
2007-11-16 11:11:20 · answer #1 · answered by ? 6 · 2⤊ 1⤋
OK
So a(-9x + 2y) - b(7x - 4y) = 46x - 20y ; lets multiply out
-9ax + 2ay - 7bx + 4by = 46x - 20y ; now let's break this apart
-9ax - 7bx = 46x ; and
2ay +4by = -20y
so : -9a -7b = 46
2a +4b = -20
Now we have two equations two unknowns. Mutiply the top equation by 4 and the bottom by 7 to get rid of b
-36a - 28b = 184
14a +28b = -140 ; add the equations
-22a = 44
a = -2
Now place a back into the first equation:
-9(-2) - 7b = 46
18 - 7b = 46
-7b = 28
b = -4.
So now you have a and b
a = -2
b = -4
Let do the final check in your original item
-2(-9x +2y) - (-4)(7x -4y) = 46x -20y ??
18x -4y +28x -16y = 46x - 20y ??
46x - 20y = 46x - 20y YES!!
Hope that helps.
2007-11-16 19:20:36 · answer #2 · answered by pyz01 7 · 2⤊ 0⤋
-9ax +2ay - 7bx + 4by = 46x - 20y
(-9a-7b)x + (2a+4b)y = 46x - 20y
-9a - 7b = 46
2a + 4b = -20
-18a - 14b = 92
18a + 36b = -180
22b = -88
b = -4
2a - 16 = -20
2a = -4
a = -2
2007-11-16 19:16:43 · answer #3 · answered by norman 7 · 1⤊ 0⤋
======thats so easy and i am 7 a is 400*/8/*/*=++/58=48=7/=//=//
2007-11-16 19:10:49 · answer #4 · answered by sara g 1 · 0⤊ 2⤋
im real good at math have a 97 but dont know this answer
2007-11-16 19:11:49 · answer #5 · answered by Anonymous · 0⤊ 2⤋