SOLUTION: Hi, I need some help with my math homework, its from the lesson (9-5), Multiplication with the addition-or-subtraction method (elimination method), of the algebra structure and met

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Question 864922: Hi, I need some help with my math homework, its from the lesson (9-5), Multiplication with the addition-or-subtraction method (elimination method), of the algebra structure and method book 1 by mcdougal littell.
The exercise says:
"The point (8,-3) is the intersection of the graphs ax + by = 25 and 3ax - 5by = 3. Find a and b."
PS. Please kindly explain the steps of the procedure so that I understand how to solve the question. Thank you.
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
The given point satisfies both equations.
Use the coordinate values for the point in both equations to get more specific equations:

a%2A%288%29%2Bb%2A%28-3%29=25
and
3a%2A8-5%2Ab%2A%28-3%29=3

Simplifying these gives the system:
8a-3b=25
and
24a%2B15b=3

Observe that the coefficients for a and b in the two equations are different.

ELIMINATE a TO FIND VALUE FOR b.
Multiply the "25" equation by 3, and subtract one equation from the other.
24a-9b=75.
24a-9b-%2824a%2B15b%29=75-3
-9b-15b=72
-24b=72
highlight%28b=-3%29
-
ELIMINATE b TO FIND VALUE FOR a.
Multiply the "25" equation by 5, and then add the two equations.
Here, the equivalent "25" equation becomes 40a-15b=125.
40a-15b%2B%2824a%2B15b%29=125%2B3
64a=128
highlight%28a=2%29