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 a variable and substituting that expression into the other equation.

Front

Solve using elimination: x - 2y = 4 and 3x + 2y = 4.

Back

(2, -1)

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

Solve using substitution: y = 3x + 2 and y = 2x + 3.

Back

(1, 5)

Front

Solve using substitution: y = -5x and x + 3y = 28.

Back

(-2, 10)

Front

What is a unique solution in a system of equations?

Back

A single set of values for the variables that satisfies all equations.

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.