Solving Systems of Equations

Front

What is a system of equations?

Back

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

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What does it mean to solve a system of equations?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines representing the equations.

Front

What does it mean if two lines are parallel when graphing a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

The system has infinite solutions because every point on the line is a solution.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

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What is elimination in solving systems of equations?

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Adding or subtracting equations to eliminate one variable.

Front

How do you check the solution of a system of equations?

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Substitute the solution back into the original equations to verify.

Front

What is the solution to the system of equations: x + y = 5 and x - y = 1?

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(3, 2)