Solving Systems by Substitution and Elimination

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 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 the elimination method?

Back

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

Front

How do you solve the system by elimination: 7x - 9y = 29 and 7x + 2y = -15?

Back

The solution is (-1, -4).

Front

How do you solve the system by substitution: x = -3y - 8 and x = 2y - 3?

Back

The solution is (-5, -1).

Front

How do you solve the system by substitution: y = -6x + 5 and y = 2x + 5?

Back

The solution is (0, 5).

Front

How do you solve the system by substitution: y = -x + 19 and y = 3x - 1?

Back

The solution is (5, 14).

Front

How do you solve by elimination: 7x + y = -9 and -3x - y = 5?

Back

The solution is (-1, -2).

Front

What is a consistent system of equations?

Back

A system that has at least one solution.