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Solving linear equations

Mathematics, Grade 8

Solving linear equations

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Study Guide Solving linear equations Mathematics, Grade 8

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SOLVING LINEAR EQUATIONS Linear equations are equations that have two variables. • When graphed, a linear equation is a straight line. Although the standard equation for a line is y = mx + b, where m is the slope and b is the y-intercept, linear equations often have both of the variables on the same side of the equal sign. • Linear equations can be written verbally and translated into algebraic form. • Linear equations can be solved for one variable when the other variable is given. • Since a linear equation is a straight line, the variables in the equation are points on the coordinate plane. • When a linear equation is solved, an ordered pair is the answer. Likewise, an ordered pair can be evaluated to see if it is a solution set for a linear equation. • Solving linear equations is the same as other equations and is done by the use of inverse operations. How to use solving linear equations When a linear equation is written verbally, it is important to remember that there are two variables in the equation. • For example, what is 'twice a number is increased by another number is sixty-one' in algebraic form? Ex. twice a number → 2x increased by another number → + y is sixty-one → = 61 The result is 2x + y = 61 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Once a linear equation is translated into the algebraic form, it can be solved for one of the variables if given the other variable. • For example, what is y in the equation, 2x + y = 61, when x is 19? To solve, 19 is substituted for x and the equation is solved for y. Ex. 2(19) + y = 61 → 38 + y = 61 → y = 23 The result is that x is 19 and y is 23 or (19, 23). In this case, the one variable was given and the equation was solved to find the other variable. In some cases, an ordered pair will be given to see if it is a solution set for an equation. • For example, is the ordered pair, (5, -4) a solution set for the linear equation, x - 3y = 17? Ex. x - 3y = 17 5 - 3(-4) = 17 5 + 12 = 17 17 = 17 Since the equation is true, (5, -4) is a solution set for the linear equation, x - 3y = 17. That means that the point (5, -4) is on the line x - 3y = 17. If the equation was not true it would mean that the point was not a solution set and not on the line given. Try This! 1. What is 'four times a number diminished by seven is two times another number' in algebraic form? 2. What is the value of y in the linear equation, 5x + 8 = y -2 when x is -3? 3. What is the value of y in the linear equation, 3y = -2x - 10 when y is -4? 4. Is the ordered pair, (6, -3), a solution set for the linear equation, 1/3x + 2y = 4? 5. Is the ordered pair, (10, -10), a solution set for the linear equation, 2x - 40 = 2y? © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.

Solving linear equations

Mathematics, Grade 8

Solving linear equations

Study Guide

Solving linear equations

Flash Cards

Solving linear equations

Quiz

Solving linear equations

Worksheets

Solving linear equations

Games

Study Guide Solving linear equations Mathematics, Grade 8

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