A2T - Systems 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 the graphical representation of a system of equations?

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The intersection point(s) of the lines represented by the equations on a graph.

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What is a solution to a system of equations?

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A set of values for the variables that makes all equations in the system true.

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What is the substitution method in solving systems of equations?

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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 the elimination method 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 represented by 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 determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into each equation; if all equations are satisfied, it is a solution.

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What is the first step in solving the system: 3x - y = 7 and 2x + y = 3?

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You can use either substitution or elimination; for elimination, you can add the two equations to eliminate y.