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Simplifying (y + -1tx)(8y + -1tx) = 0 Reorder the terms: (-1tx + y)(8y + -1tx) = 0 Reorder the terms: (-1tx + y)(-1tx + 8y) = 0 Multiply (-1tx + y) * (-1tx + 8y) (-1tx * (-1tx + 8y) + y(-1tx + 8y)) = 0 ((-1tx * -1tx + 8y * -1tx) + y(-1tx + 8y)) = 0 Reorder the terms: ((-8txy + 1t2x2) + y(-1tx + 8y)) = 0 ((-8txy + 1t2x2) + y(-1tx + 8y)) = 0 (-8txy + 1t2x2 + (-1tx * y + 8y * y)) = 0 (-8txy + 1t2x2 + (-1txy + 8y2)) = 0 Reorder the terms: (-8txy + -1txy + 1t2x2 + 8y2) = 0 Combine like terms: -8txy + -1txy = -9txy (-9txy + 1t2x2 + 8y2) = 0 Solving -9txy + 1t2x2 + 8y2 = 0 Solving for variable 't'. Factor a trinomial. (tx + -8y)(tx + -1y) = 0Subproblem 1
Set the factor '(tx + -8y)' equal to zero and attempt to solve: Simplifying tx + -8y = 0 Solving tx + -8y = 0 Move all terms containing t to the left, all other terms to the right. Add '8y' to each side of the equation. tx + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 tx + 0 = 0 + 8y tx = 0 + 8y Remove the zero: tx = 8y Divide each side by 'x'. t = 8x-1y Simplifying t = 8x-1ySubproblem 2
Set the factor '(tx + -1y)' equal to zero and attempt to solve: Simplifying tx + -1y = 0 Solving tx + -1y = 0 Move all terms containing t to the left, all other terms to the right. Add 'y' to each side of the equation. tx + -1y + y = 0 + y Combine like terms: -1y + y = 0 tx + 0 = 0 + y tx = 0 + y Remove the zero: tx = y Divide each side by 'x'. t = x-1y Simplifying t = x-1ySolution
t = {8x-1y, x-1y}
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