Systems of Equations and Inequalities

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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.

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap on a graph.

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

Back

It means that the lines representing 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 that the lines representing the equations are parallel and never intersect.

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

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

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How do you represent a system of equations graphically?

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You graph each equation on the same coordinate plane and look for points of intersection.

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

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

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What is the standard form of a linear equation?

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The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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How do you solve a system of equations using substitution?

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You solve one equation for one variable and substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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You add or subtract the equations to eliminate one variable, making it easier to solve for the other.