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 adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

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

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine if a system of equations has one solution?

Back

If the lines represented by the equations intersect at exactly one point.

Front

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

Back

(7, 0)

Front

Solve by substitution: 5x + 4y = -14 and y = -7x - 15

Back

(-2, -1)

Front

Solve by elimination: 4x + 4y = 4 and 3x + 4y = 10

Back

(-6, 7)