6-5 Systems of Equations (Graphs and Substitution)

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 for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

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What does it mean for a system of equations to have no solution?

Back

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

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What does it mean for a system of equations to have infinite solutions?

Back

It means that the equations represent the same line, so there are countless points that satisfy both equations.

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How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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How do you graph a system of equations?

Back

1. Graph each equation on the same coordinate plane. 2. Identify the point(s) where the lines intersect.

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What is the substitution method?

Back

A method for solving systems of equations by expressing one variable in terms of the other and substituting it into the second equation.

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What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

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What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How can you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If both equations are true, the point is a solution.