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Simplifying 1 + -1x2 = 4 + -4y2 Solving 1 + -1x2 = 4 + -4y2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x2 = 4 + -1 + -4y2 Combine like terms: 1 + -1 = 0 0 + -1x2 = 4 + -1 + -4y2 -1x2 = 4 + -1 + -4y2 Combine like terms: 4 + -1 = 3 -1x2 = 3 + -4y2 Divide each side by '-1'. x2 = -3 + 4y2 Simplifying x2 = -3 + 4y2 Reorder the terms: 3 + x2 + -4y2 = -3 + 4y2 + 3 + -4y2 Reorder the terms: 3 + x2 + -4y2 = -3 + 3 + 4y2 + -4y2 Combine like terms: -3 + 3 = 0 3 + x2 + -4y2 = 0 + 4y2 + -4y2 3 + x2 + -4y2 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 3 + x2 + -4y2 = 0 Factor a trinomial. (x + -1y)(x + 4y) = 0Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySubproblem 2
Set the factor '(x + 4y)' equal to zero and attempt to solve: Simplifying x + 4y = 0 Solving x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 x + 0 = 0 + -4y x = 0 + -4y Remove the zero: x = -4y Simplifying x = -4ySolution
x = {y, -4y}
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