SOLUTION: Im not sure if I've put this into the right catagory but heres the question: Given that: a(3x + 2) + b(4x - 5) = 34x - 31 Work out the values of a and b. Thankyou :)

Algebra ->  Expressions-with-variables -> SOLUTION: Im not sure if I've put this into the right catagory but heres the question: Given that: a(3x + 2) + b(4x - 5) = 34x - 31 Work out the values of a and b. Thankyou :)       Log On


   

Question 417429: Im not sure if I've put this into the right catagory but heres the question:
Given that: a(3x + 2) + b(4x - 5) = 34x - 31
Work out the values of a and b.
Thankyou :)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Given that: a(3x + 2) + b(4x - 5) = 34x - 31
Work out the values of a and b.
Hopefully we are dealing with integers here
:
Write an equation for the sum of the coefficient of x; 34
3a + 4b = 34
:
write an equation for sum of -31
2a - 5b = -31
:
Multiply the 1st equation by 5, the 2nd equation by 4, we have
15a + 20b = 170
8a - 20b = -124
--------------------adding eliminates b, find a
23a = 46
a = 46/23
a = 2
:
find b using the equation 3a + 4b = 34
3(2) + 4b = 34
6 + 4b = 34
4b = 34 - 6
4b = 28
b = 28/4
b = 7
:
a=2; b=7
:
see if that works
2(3x + 2) + 7(4x - 5) = 34x - 31
6x + 4 + 28x - 35 = 34x - 31
Combine like terms
34x - 31 = 34x - 31; confirms our solution
:
did this make sense to you here?