Systems of Equations: Graphing and Substitution

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 one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and never intersect.

Front

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

Back

The lines coincide, meaning they are the same line.

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 using substitution: 2y + x = -15, x = 3y

Back

(-9, -3)

Front

Solve the system: y = 4x - 10, y = 3x - 5

Back

(5, 10)

Front

What is the first step in solving a system of equations by graphing?

Back

Graph both equations on the same coordinate plane.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

Solve: y = 3x - 2, 2x + 3y = 38

Back

x = 4