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 removing one variable, allowing for easier solving.

Front

Solve using elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1)

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

Solve using substitution: y = 2x + 11 and -3x + 4y = 29.

Back

(-3, 5)

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

Solve the system: -3x - 3y = 3 and y = -5x - 17.

Back

(-4, 3)

Front

What is a consistent system of equations?

Back

A system that has at least one solution.