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Solve for x and y: System of Equations (x-2)(y+5)=(x-1)(y+2) and (y-3)(x+4)=(x+7)(y-4)
Published on August 2, 2024
Algebra
Solve for x and y in the system of equations: (x-2)(y+5)=(x-1)(y+2) and (y-3)(x+4)=(x+7)(y-4). The solution is x=5 and y=7.
Question
x=? y=?
Answer
Let’s solve for x and y step-by-step.
1. Expand both equations:
-
Equation 1:
(x - 2)(y + 5) = (x - 1)(y + 2)
xy + 5x - 2y - 10 = xy + 2x - y - 2 -
Equation 2:
(y - 3)(x + 4) = (x + 7)(y - 4)
xy + 4y - 3x - 12 = xy - 4x + 7y - 28
2. Simplify both equations:
-
Equation 1:
3x - y = 8 -
Equation 2:
x - 3y = -16
3. Solve for one variable in terms of the other (let’s solve for x in Equation 2):
- Equation 2:
x = 3y - 16
4. Substitute the value of x from Equation 2 into Equation 1:
- 3(3y - 16) - y = 8
5. Simplify and solve for y:
- 9y - 48 - y = 8
- 8y = 56
- y = 7
6. Substitute the value of y back into either Equation 1 or 2 to solve for x (let’s use Equation 2):
- x = 3(7) - 16
- x = 21 - 16
- x = 5
Answer:
- x = 5
- y = 7