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Simplifying 2x2 + 6y2 = 8 Solving 2x2 + 6y2 = 8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6y2' to each side of the equation. 2x2 + 6y2 + -6y2 = 8 + -6y2 Combine like terms: 6y2 + -6y2 = 0 2x2 + 0 = 8 + -6y2 2x2 = 8 + -6y2 Divide each side by '2'. x2 = 4 + -3y2 Simplifying x2 = 4 + -3y2 Reorder the terms: -4 + x2 + 3y2 = 4 + -3y2 + -4 + 3y2 Reorder the terms: -4 + x2 + 3y2 = 4 + -4 + -3y2 + 3y2 Combine like terms: 4 + -4 = 0 -4 + x2 + 3y2 = 0 + -3y2 + 3y2 -4 + x2 + 3y2 = -3y2 + 3y2 Combine like terms: -3y2 + 3y2 = 0 -4 + x2 + 3y2 = 0 Factor a trinomial. (x + -3y)(x + -1y) = 0Subproblem 1
Set the factor '(x + -3y)' equal to zero and attempt to solve: Simplifying x + -3y = 0 Solving x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 x + 0 = 0 + 3y x = 0 + 3y Remove the zero: x = 3y Simplifying x = 3ySubproblem 2
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 = ySolution
x = {3y, y}
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