Systems of Equations - Elimination + Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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 simultaneously.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one 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 do not intersect.

Front

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

Back

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

Front

Solve the system: 3x - y = 4 and 2x - 3y = -9

Back

(3, 5)

Front

Solve the system: 5x + y = 9 and 10x - 7y = -18 using elimination.

Back

(1, 4)

Front

Solve by elimination: 7x - 9y = 29 and 7x + 2y = -15

Back

(-1, -4)

Front

What is the first step in the elimination method?

Back

Align the equations so that like terms are in the same column.