Systems of equations: graphing, substitution, elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have a solution?

Back

It means there is at least one ordered pair (x, y) that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The point(s) where the graphs of the equations intersect.

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

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

It means the system has no solutions because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

It means the system has infinitely many solutions because the lines are the same.

Front

How do you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

Solve the system: 2x + 3y = -2 and 3x - 2y = 23.

Back

(5, -4)

Front

Solve the system: x + y = 19 and y = 3x - 1.

Back

(5, 14)