Solving Systems by Substitution

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What is a system of linear equations?

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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 by substitution?

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

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

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Make sure at least one equation is solved for one variable.

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

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Substitute the solution back into both original equations to see if both equations are satisfied.

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What is the slope-intercept form of a linear equation?

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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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