Systems of Equations Basics Review

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What is a system of equations?

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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.

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What does it mean if a system of equations has one solution?

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It means the lines represented by the equations intersect at exactly one point.

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

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It means the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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It means the lines represented by the equations are the same line, so they intersect at every point on that line.

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

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

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise over the run (change in y over change in x).

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What are parallel lines?

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Parallel lines are lines in a plane that never meet. They have the same slope.

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What are perpendicular lines?

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Perpendicular lines are lines that intersect at a right angle. Their slopes are opposite reciprocals.

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How do you solve a system of equations by graphing?

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Graph both equations on the same coordinate plane and identify the point(s) where they intersect.

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.