Solving Systems by Substitution

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What is a system of equations?

Back

A system of equations is a set of two or more 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.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation.

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What is the first step in solving the system: x = 3y - 13 and 4x + 2y = 4?

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Substitute the expression for x from the first equation into the second equation.

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

Back

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 infinite 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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Back

The solution is (-3, 1).

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What is the substitution method used for?

Back

The substitution method is used to find the values of variables in a system of equations.

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

Back

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

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Back

The solution is (-3, -2).