Solving Systems of Equations

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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 one solution?

Back

It means that the graphs of the equations intersect at exactly one point.

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

Back

It means that the graphs of the equations are parallel and never intersect.

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

Back

It means that the equations represent the same line, so they intersect at every point on that line.

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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 solve a system of equations using elimination?

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1. Align the equations. 2. Add or subtract the equations to eliminate one variable. 3. Solve for the remaining variable.

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What is the graphical representation of a system of equations?

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The graphical representation consists of the lines of the equations plotted on a coordinate plane.

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What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, where all equations are satisfied.

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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 point's coordinates into each equation. If both equations are true, the point is a solution.