Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear 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 infinitely many solutions?

Back

The lines representing the equations are the same line, overlapping each other.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

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 by elimination: 2x + 3y = 6 and 4x - 3y = 12.

Back

(3,0)

Front

Solve by substitution: y = 2x + 3 and y = -x + 1.

Back

(-1,1)

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at a single point.

Front

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

Back

Two parallel lines that never intersect.