Systems of Equations & Inequalities Review

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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 does it mean for a point to be a solution to a system of equations?

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A point is a solution to a system of equations if it satisfies all equations in the system, meaning it makes all equations true when substituted.

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

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What is the difference between '>' and '≥'?

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'>' means greater than, while '≥' means greater than or equal to.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line. Then, use a dashed line for '>' or '<' and a solid line for '≥' or '≤'. Shade the region that satisfies the inequality.

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

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A system of equations has no solution if the lines representing 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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A system of equations has infinitely many solutions if the equations represent the same line, meaning 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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To determine if a point is a solution, substitute the x and y values of the point into each equation. If the equations hold true, the point is a solution.

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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 then substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.