Unit 5- Systems of Equations Review for Test

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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 on a graph.

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What does it mean if two linear equations represent the same line?

Back

If two linear equations represent the same line, it means they have infinitely many solutions, as every point on the line is a solution.

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How do you find the slope of a line from an equation in slope-intercept form?

Back

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Back

The slope of the line is 4.

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Back

The y-intercept is 6, which is the point where the line crosses the y-axis.

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How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines are parallel, meaning they have the same slope but different y-intercepts.

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Back

The solution is the point (4, 14).

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What does it mean for a system of equations to have exactly one solution?

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A system has exactly one solution if the lines intersect at a single point, meaning they have different slopes.

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How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable and substitute that expression into the other equation.

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Back

The solution is the ordered pair (4, -1).