Systems of Equations by Graphing

Front

What are systems of equations?

Back

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

Front

What does it mean for lines to be parallel?

Back

Parallel lines never intersect and have the same slope.

Front

What is the slope-intercept form of a line?

Back

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

Front

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

Back

Graph both equations on the same coordinate plane and identify the point where they intersect.

Front

What does the intersection point of two lines represent in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

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

Back

(1, 3)

Front

What does it mean if two lines have different slopes?

Back

If two lines have different slopes, they will intersect at one point, indicating a unique 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.