SOLUTION: Solve the folllowing system of equations algebraically: 3x+2y=4 4x+3y=7

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Question 288639: Solve the folllowing system of equations algebraically:
3x+2y=4
4x+3y=7

Answer by brucewill(101) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to eliminate one variable or the other; I'm choosing to eliminate x, by multiplying the first statement by 4, and the second statement by 3:
12x+%2B+8y+=+16
12x+%2B+9y+=+21
Now, subtract the first statment from the first:
highlight%28y+=+5%29
Substitute for y into either equation (I choose the second)
12x+%2B+45+=+21
12x+=+-24
highlight%28x+=+-2%29
To prove, substitute into both equations:
3(-2) + 2(5) = 16
-6 + 10 = 4
16 = 16.
4(-2) + 3(5) = 7
-8 + 15 = 7
7 = 7.