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Simplifying 2(5p + -1q) + -1(p + -3q) = 0 (5p * 2 + -1q * 2) + -1(p + -3q) = 0 (10p + -2q) + -1(p + -3q) = 0 10p + -2q + (p * -1 + -3q * -1) = 0 10p + -2q + (-1p + 3q) = 0 Reorder the terms: 10p + -1p + -2q + 3q = 0 Combine like terms: 10p + -1p = 9p 9p + -2q + 3q = 0 Combine like terms: -2q + 3q = 1q 9p + 1q = 0 Solving 9p + 1q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. 9p + 1q + -1q = 0 + -1q Combine like terms: 1q + -1q = 0 9p + 0 = 0 + -1q 9p = 0 + -1q Remove the zero: 9p = -1q Divide each side by '9'. p = -0.1111111111q Simplifying p = -0.1111111111q
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