(4, 4/3)
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To solve for (x,y) using the elimination method, we aim to eliminate one variable to solve for the other. Let's start by rewriting the given system of equations:
- 3y = 20 - 4x ...(1)
- 2y = 12 - 3x ...(2)
First, to make the coefficients of y the same, we can multiply equation (1) by 2 and equation (2) by 3:
- 2*(3y) = 2*(20 - 4x) => 6y = 40 - 8x ...(3)
- 3*(2y) = 3*(12 - 3x) => 6y = 36 - 9x ...(4)
With both equations now having the same coefficient for y, we can subtract equation (4) from equation (3):
- (40 - 8x) - (36 - 9x) = 0
- 40 - 8x - 36 + 9x = 0
- 4 - x = 0
- x = 4
Now we know the value of x, we can substitute it back into either equation (1) or (2) to find y:
- 3y = 20 - 4*4
- 3y = 20 - 16
- 3y = 4
- y = 4/3
The solution to the system of equations is (x, y) = (4, 4/3).
