Unit 5 - Solving Systems of Linear Equations by Substitution

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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear 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 by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

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The solution is (2, 1).

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What does it mean if two lines represented by a system of equations intersect at one point?

Back

It means the system has a unique solution, which is the point of intersection.

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Back

The solution is (1, 1).

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What is the graphical representation of a system of equations with no solution?

Back

The lines are parallel and never intersect.

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The solution is (4, 2).

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What does it indicate if a system of equations has infinitely many solutions?

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It indicates that the equations represent the same line, and every point on the line is a solution.