Systems of Equations and 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 to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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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 represented by the equations on a coordinate plane.

Front

What is an inequality?

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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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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 shade the region that satisfies the inequality.

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What is the difference between a linear equation and a linear inequality?

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A linear equation shows equality (e.g., y = mx + b), while a linear inequality shows a range of values (e.g., y < mx + b).

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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 equations 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 equations represent parallel lines that never 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.

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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.