# Solving Sets of Linear Equations 1.pdf - MATH 10005 SOLVING...

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MATH 10005 SOLVING LINEAR EQUATIONS KSU Definition : A linear equation in one variable can be written in the form ax + b = c for real numbers a, b, and c , with a 6 = 0. Important Properties : Addition Property of Equality: If a, b, and c are real numbers, then a = b and a + c = b + c are equivalent equations. (That is, you can add or subtract the same quantity on both sides of the equation without changing the solution.) Multiplication Property of Equality: If a, b, and c are real numbers and c 6 = 0, then a = b and ac = bc are equivalent equations. (That is, you can multiply or divide the same nonzero quantity on both sides of the equation without changing the solution.) Common Mistakes to Avoid : When clearing the parentheses in an expression like 7 - (2 x - 4), remember that the minus sign acts like a factor of - 1. After using the distributive property, the sign of every term in the parentheses will be changed to give 7 - 2 x + 4. To clear fractions from an equation, multiply every term on each side by the lowest common de- nominator. Remember that