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

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
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