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Simplifying 4(x + -2y) + -1(y + -3x) = 4(x + -2y) + -1(y + -3x) (x * 4 + -2y * 4) + -1(y + -3x) = 4(x + -2y) + -1(y + -3x) (4x + -8y) + -1(y + -3x) = 4(x + -2y) + -1(y + -3x) Reorder the terms: 4x + -8y + -1(-3x + y) = 4(x + -2y) + -1(y + -3x) 4x + -8y + (-3x * -1 + y * -1) = 4(x + -2y) + -1(y + -3x) 4x + -8y + (3x + -1y) = 4(x + -2y) + -1(y + -3x) Reorder the terms: 4x + 3x + -8y + -1y = 4(x + -2y) + -1(y + -3x) Combine like terms: 4x + 3x = 7x 7x + -8y + -1y = 4(x + -2y) + -1(y + -3x) Combine like terms: -8y + -1y = -9y 7x + -9y = 4(x + -2y) + -1(y + -3x) 7x + -9y = (x * 4 + -2y * 4) + -1(y + -3x) 7x + -9y = (4x + -8y) + -1(y + -3x) Reorder the terms: 7x + -9y = 4x + -8y + -1(-3x + y) 7x + -9y = 4x + -8y + (-3x * -1 + y * -1) 7x + -9y = 4x + -8y + (3x + -1y) Reorder the terms: 7x + -9y = 4x + 3x + -8y + -1y Combine like terms: 4x + 3x = 7x 7x + -9y = 7x + -8y + -1y Combine like terms: -8y + -1y = -9y 7x + -9y = 7x + -9y Add '-7x' to each side of the equation. 7x + -7x + -9y = 7x + -7x + -9y Combine like terms: 7x + -7x = 0 0 + -9y = 7x + -7x + -9y -9y = 7x + -7x + -9y Combine like terms: 7x + -7x = 0 -9y = 0 + -9y -9y = -9y Add '9y' to each side of the equation. -9y + 9y = -9y + 9y Combine like terms: -9y + 9y = 0 0 = -9y + 9y Combine like terms: -9y + 9y = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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