Solving 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 two lines are parallel in a system of equations?

Back

The system has no solution because the lines never intersect.

Front

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

Back

The system has infinitely many solutions because the lines overlap completely.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is slope-intercept form?

Back

The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

Convert the equation 3x + 2y = 12 into slope-intercept form.

Back

y = -1.5x + 6.

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.

Front

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

Back

Two identical lines that overlap completely.

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.