Systems of Equations Graphing

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 on a graph?

Back

It means that the two equations have a common solution, represented by the point of intersection.

Front

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

Back

By graphing both equations and identifying the point where they intersect.

Front

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

Back

(-1, -2)

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 does the slope of a line represent?

Back

The rate of change of y with respect to x.

Front

What is the y-intercept of the equation y = 6x - 4?

Back

-4, which is the point where the line crosses the y-axis.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

What is the graphical representation of the equation y = -x + 3?

Back

A straight line with a slope of -1 and a y-intercept of 3.

Front

What does it mean if two lines are parallel?

Back

They have the same slope but different y-intercepts, meaning they never intersect.