Systems of Linear Equations Review

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What is a system of linear equations?

Back

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 linear equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

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What is the substitution method?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the graphing method?

Back

A method of solving systems of equations by graphing the equations on the same coordinate plane and identifying the intersection point.

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What is the equal values method?

Back

A method where two equations are set equal to each other to find the variable values.

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How do you determine if a system of equations has no solution?

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If the lines represented by the equations are parallel, they will never intersect, indicating no solution.

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How do you determine if a system of equations has infinitely many solutions?

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If the equations represent the same line, every point on the line is a solution, indicating infinitely many solutions.

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What is the solution to the system of equations: x + 2y = -3 and x - y = -12?

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(-9, 3) is the solution.

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What is the solution to the system of equations: 5x + 3y = 8 and 3x - 3y = 0?

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(1, 1) is the solution.