Solving Systems of Equations Graphically

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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 to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect.

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What is the solution of a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

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What does it mean if two lines are parallel in a system of equations?

Back

It means there is no solution, as the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

Back

It means there are infinitely many solutions, as every point on the line is a solution.

Front

How do you identify the solution from a graph?

Back

Look for the point where the two lines intersect; that point is the solution.

Front

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

Back

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Back

The y-intercept is 3, which is the point (0, 3) on the graph.

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Back

The slope is -1/2, indicating the line falls as it moves from left to right.

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How can you determine if a system of equations has one solution?

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If the lines intersect at exactly one point, the system has one solution.