# Thread: system of equations

1. ## system of equations

Hello, I am wondering if I have gone about this system of equations correctly ?

3x+5 = AX+2A+BX+B

using x = 0
5 = 2A+B

using x = 1
8 = 3A + 2B

therefore:
5 = 2A+B
8 = 3A + 2B

cancelling a term:
10 = 4A+2B
8 = 3A + 2B

equals:
A = 2
B= 1

2. ## Re: system of equations

Hello, fran1942!

Hello, I am wondering if I have gone about this system of equations correctly ?

3x+5 = AX+2A+BX+B

using x = 0
5 = 2A+B

using x = 1
8 = 3A + 2B

therefore:
5 = 2A+B
8 = 3A + 2B

cancelling a term:
10 = 4A+2B
8 = 3A + 2B

equals:
A = 2
B= 1

You're absolutely correct! . . . Good work!

Here's another approach . . .

We have: .$\displaystyle 3x + 5 \:=\:(A+B)x + (2A+B)$

Two polynomials are equal if their corresponding coefficients are equal.

Hence: .$\displaystyle \begin{Bmatrix}A + B &=& 3 \\ 2A + B &=& 5 \end{Bmatrix}$

which yields the same answers: .$\displaystyle \begin{Bmatrix} A &=& 2 \\ B &=& 1 \end{Bmatrix}$

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