Systems of Equations - Word Problems

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other.

Front

What does it mean for two variables to be directly proportional?

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Two variables are directly proportional if they increase or decrease at the same rate, represented by the equation y = kx, where k is a constant.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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How can you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

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What is a consistent system of equations?

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A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system has infinitely many solutions, meaning the equations represent the same line.

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How do you interpret the solution of a system of equations in a word problem?

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The solution represents the values of the variables that satisfy all conditions of the problem.