Solving Linear Systems: Graphing, Substitution, Elimination

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What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

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What does it mean to solve a linear system?

Back

To solve a linear system means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What are the three methods to solve a linear system?

Back

The three methods are Graphing, Substitution, and Elimination.

Front

What is the substitution method?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the graphing method?

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The graphing method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

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What does it mean if a linear system has no solution?

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A linear system has no solution if the lines represented by the equations are parallel and never intersect.

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What does it mean if a linear system has infinitely many solutions?

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A linear system has infinitely many solutions if the equations represent the same line, meaning they overlap completely.

Front

How do you check the solution of a linear system?

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To check the solution, substitute the values back into the original equations to see if they hold true.

Front

What is the solution to the system: -x + 5y = 12 and y = -2x - 2?

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The solution is (-2, 2).