Solving System of Equations

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What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is an ordered pair?

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A pair of numbers (x, y) that represent a point on a coordinate plane.

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How do you graph a system of equations?

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By plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

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What is the solution to a system of equations?

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The point(s) where the graphs of the equations intersect, representing the values of the variables.

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What is substitution in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is elimination in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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

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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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The equations represent the same line, meaning every point on the line is a solution.

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How do you check the solution of a system of equations?

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By substituting the solution back into the original equations to see if they hold true.