Solving Systems by Substitution

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What is a system of linear equations?

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A set of two or more linear equations with the same variables.

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What does it mean to solve a system of equations by substitution?

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It means to solve one equation for one variable and then substitute that expression into the other equation.

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What is the first step in solving a system of equations by substitution?

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Isolate one variable in one of the equations.

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(2, 1)

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

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It means 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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It means the equations represent the same line, so every point on the line is a solution.

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How do you check if your solution to a system of equations is correct?

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Substitute the solution back into both original equations to see if they hold true.

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What is the graphical representation of a system of equations?

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It is the intersection point(s) of the lines represented by the equations.

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What is the substitution method?

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A method for solving systems of equations by expressing one variable in terms of the other.