How to Solve Word Problems Using Linear Equations

Written by renee price
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How to Solve Word Problems Using Linear Equations
Math word problems can be intimidating; the most challenging part is translating the wording to mathematical equations. (Formule image by wally from

Many people find math intimidating, and in particular, word problems. Solving word problems with linear equations, problems with more than one unknown variable, seems almost impossible to some people. No matter your age or profession, math and problem solving is everywhere, and you're bound to come face to face with the challenge of solving word problems at some point. Translating word problems from English to actual mathematical equations is the prevalent stumbling block most people face. However, once you construct the equation, solving for the answer is relatively straightforward.

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  1. 1

    Read the problem thoroughly to understand what you are solving. List all of the unknowns in the problem, and assign a variable for each unknown. If there are two unknowns, you need two variables, such as x and y, for example. If there are three unknowns, you need three variables, such as x, y and z. The number of unknowns in the word problem also indicates the number of equations required. It may help to name the variables so they reflect the unknowns you're solving. For example, if you're solving a problem dealing with an unknown number of apples and pears, use "a" as the variable for apples, and use "p" as the variable for pears.

  2. 2

    Translate the problem into a system of equations using key terms to describe the operations required. Terms such as "increased by" or "total of" signal operations that involve addition. Phrases such as "decreased by" or "difference between" means the operations involve subtraction. Words and phrases such as "of", "product of" or "times" indicate operations that require multiplication. Terms such as "per" or "out of" indicate operations that require division. When words like "is" or "will be" are featured in a word problem, this indicates the amount unknown expressions must equal.

  3. 3

    Solve the equations using graphical, substitution or elimination methods.

    Draw the first equation on a coordinate system graph, then draw the second equation on the same coordinate system. If the two lines intersect, the point of intersection is the solution. If the two lines run parallel, there is no solution. If the two lines are on top of each other, there are infinite solutions.

    Solve with the substitution method by solving the first equation for one variable, then substitute the expression into the equation you didn't use. Solve the equation with the substituted equation for the remaining unknown variable.

    Use the elimination method by multiplying one or both of the equations by a number that creates opposite coefficients for one variable. For example, if you have two equations:

    5x + 3y = 30

    2x + 3y = -3

    Multiply the second equation by negative one to create opposite coefficients for the "y" variable shared between each equation. Add the equations together to eliminate the "y" variable, and solve for the remaining variable. Plug the answer for the solved variable into one of the equations to solve for the second variable that was eliminated.

  4. 4

    Check the proposed solution by plugging the answers in to each equation. If both sides of each equation are equal, you have the solution. If one side of the equation does not equal the other, check your work and redo the problem.

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