SOLUTION: Please help me solve the question below. Find the values of the constants a and b if 3x+5=a(x-1)+b(2x+3), for all x�R

Question 98330: Please help me solve the question below.
Find the values of the constants a and b if
3x+5=a(x-1)+b(2x+3), for all x�R
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the values of the constants a and b if
3x+5=a(x-1)+b(2x+3), for all x�R
----------------
3x+5 = ax-a+2bx+3b
3x+5 = (a+2b)x+(-a+3b)
-------------
Equating the corresponding coefficients you get:
a+2b=3
-a+3b=5
---------
Add the two equations to get:
5b=8
b=8/5
---------
Subtitute into a+2b=3 to solve for "a":
a+2(8/5)=3
a+16/5 = 15/5
a = -1/5
=================
Check the answer in -a+3b=5
1/5 + 3(8/5) = 5
1/5 +24/5 = 5
5=5
========
Cheers,
Stan H.
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