Solving Systems of Equations

Front

What is a system of equations?

Back

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

Front

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 elimination method?

Back

A technique for solving systems of equations by eliminating one variable, making it easier to solve for the other.

Front

How do you use the elimination method?

Back

1. Align the equations. 2. Multiply if necessary to match coefficients. 3. Add or subtract equations to eliminate one variable.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

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What is an inconsistent system of equations?

Back

A system that has no solutions.

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What is a dependent system of equations?

Back

A system that has infinitely many solutions, where the equations represent the same line.

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

Solve the system: x + y = 19 and y = 3x - 1.

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(5, 14)