Graphing 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 for two lines to intersect?

Back

It means they have one solution, which is the point where they cross.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

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 of intersection.

Front

What does it mean if two lines are parallel?

Back

They have no solutions because they never intersect.

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

What is the y-intercept of the equation y = 2x + 1?

Back

1, because it is the value of y when x = 0.

Front

What is the slope of the equation y = 4x - 1?

Back

4, which indicates the steepness of the line.

Front

If a system of equations has no solution, what does this indicate about the lines?

Back

The lines are parallel.

Front

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

Back

(1, 3) - the point where the two lines intersect.