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 if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are the same line, overlapping completely.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

Solve the system by substitution: 5x + 4y = -14, y = -7x - 15

Back

(-2, -1)

Front

Solve the system by substitution: 2y + x = -15, x = 3y

Back

(-9, -3)

Front

When graphing the same equation twice, what is the result?

Back

You will have infinite solutions.

Front

Solve the system by substitution: y = -6x + 5, -2x + y = 5

Back

(0, 5)

Front

What is the graphical representation of a system with no solution?

Back

Two parallel lines that never intersect.