Solve Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean when a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

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What does it mean when a system of equations has infinite solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

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How do you represent a system of equations graphically?

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By plotting the equations on a coordinate plane and looking for points of intersection.

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What is substitution in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

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What is elimination in solving systems of equations?

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A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical representation of the equations 3x + 2y = 315 and 2x + 4y = 450?

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The lines intersect at a point, indicating a unique solution.

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What is the significance of the statement 4 = 7 in a system of equations?

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It indicates that there is no solution, as this statement is false.

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What does the equation 2 = 2 signify in a system of equations?

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It indicates that there are infinite solutions, as this statement is always true.

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What is the first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.