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Simplifying 3(5y + -7a) + 5(3a + -7y) = 7(5y + -3a) Reorder the terms: 3(-7a + 5y) + 5(3a + -7y) = 7(5y + -3a) (-7a * 3 + 5y * 3) + 5(3a + -7y) = 7(5y + -3a) (-21a + 15y) + 5(3a + -7y) = 7(5y + -3a) -21a + 15y + (3a * 5 + -7y * 5) = 7(5y + -3a) -21a + 15y + (15a + -35y) = 7(5y + -3a) Reorder the terms: -21a + 15a + 15y + -35y = 7(5y + -3a) Combine like terms: -21a + 15a = -6a -6a + 15y + -35y = 7(5y + -3a) Combine like terms: 15y + -35y = -20y -6a + -20y = 7(5y + -3a) Reorder the terms: -6a + -20y = 7(-3a + 5y) -6a + -20y = (-3a * 7 + 5y * 7) -6a + -20y = (-21a + 35y) Solving -6a + -20y = -21a + 35y Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '21a' to each side of the equation. -6a + 21a + -20y = -21a + 21a + 35y Combine like terms: -6a + 21a = 15a 15a + -20y = -21a + 21a + 35y Combine like terms: -21a + 21a = 0 15a + -20y = 0 + 35y 15a + -20y = 35y Add '20y' to each side of the equation. 15a + -20y + 20y = 35y + 20y Combine like terms: -20y + 20y = 0 15a + 0 = 35y + 20y 15a = 35y + 20y Combine like terms: 35y + 20y = 55y 15a = 55y Divide each side by '15'. a = 3.666666667y Simplifying a = 3.666666667y
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