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Simplifying 6(9a + -9y) + 8(3x + 2y) = 0 (9a * 6 + -9y * 6) + 8(3x + 2y) = 0 (54a + -54y) + 8(3x + 2y) = 0 54a + -54y + (3x * 8 + 2y * 8) = 0 54a + -54y + (24x + 16y) = 0 Reorder the terms: 54a + 24x + -54y + 16y = 0 Combine like terms: -54y + 16y = -38y 54a + 24x + -38y = 0 Solving 54a + 24x + -38y = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-24x' to each side of the equation. 54a + 24x + -24x + -38y = 0 + -24x Combine like terms: 24x + -24x = 0 54a + 0 + -38y = 0 + -24x 54a + -38y = 0 + -24x Remove the zero: 54a + -38y = -24x Add '38y' to each side of the equation. 54a + -38y + 38y = -24x + 38y Combine like terms: -38y + 38y = 0 54a + 0 = -24x + 38y 54a = -24x + 38y Divide each side by '54'. a = -0.4444444444x + 0.7037037037y Simplifying a = -0.4444444444x + 0.7037037037y
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