Systems of Equations

Front

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

Back

The two lines intersect at one point.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

What do you call a system of equations that has no solution?

Back

An inconsistent system.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The two lines are the same line.

Front

How can you determine if two lines are parallel when given their equations?

Back

If their slopes are equal and their y-intercepts are different.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable and 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.

Front

What does it mean if two lines intersect at a point?

Back

The system of equations has one unique solution.

Front

What is the solution to the system of equations: 3x + 2y = 12 and 6x - 4y = 0?

Back

(2, 3)