Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run (change in y over change in x).

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What is the slope of a line perpendicular to a line with slope m?

Back

The slope of the perpendicular line is -1/m.

Front

If y = 2x + 1, what is the slope?

Back

The slope is 2.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

How can you solve a system of equations using substitution?

Back

By solving one equation for one variable and substituting that expression into the other equation.