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 one solution?

Back

The lines represented by the equations intersect at exactly one point.

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 lines represented by the equations are the same line, overlapping each other.

Front

Solve the system of equations: -x + y = -13 and -8x - 4y = -8.

Back

(5, -8)

Front

Solve the system of equations: y = 4x + 1 and 3x + 2y = 13.

Back

(1, 5)

Front

Solve the system of equations: y = 2/3x - 2 and y = -x + 3.

Back

(3, 0)

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane.

Front

How can you determine the number of solutions in a system of equations graphically?

Back

By observing the intersection points of the lines.

Front

What is the substitution method in solving systems of equations?

Back

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