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 two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines are the same in a system of equations?

Back

There are infinitely many solutions because every point on the line is a solution.

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

Back

(-9, -3)

Front

Solve the system using substitution: y = 4x + 1, 3x + 2y = 13

Back

(1, 5)

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines represented by the equations.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel, they do not intersect.

Front

What is the solution to the system of equations: y = 8x + 1, y = 6x + 3?

Back

(1, 9)

Front

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

Back

The lines intersect at exactly one point.