Systems of Equations and Inequalities 2024

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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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How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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What is the graphical representation of a system of equations?

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The graphical representation is the intersection point(s) of the lines representing each equation on a coordinate plane.

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What does it mean for a system of equations to be consistent?

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A consistent system has at least one solution, meaning the lines intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system has no solutions, meaning the lines are parallel and never 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.

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How do you graph a linear inequality?

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1. Graph the boundary line (dashed for < or >, solid for ≤ or ≥). 2. Shade the region that satisfies the inequality.

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What is the difference between '≤' and '<'?

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'≤' means less than or equal to, including the boundary. '<' means strictly less than, excluding the boundary.

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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 value 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.