System of Equations - Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by graphing?

Back

Solving a system of equations by graphing involves plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the solution to the system of equations y = 1/2x + 2 and y = -3x + 9?

Back

(2, 3)

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept is found by setting x = 0 in the equation and solving for y.

Front

What is the slope of the line represented by the equation y = 1/2x + 2?

Back

The slope is 1/2.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of the equation y = -3x + 9?

Back

The y-intercept is 9.

Front

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

Back

(1, 3)

Front

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

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system.

Front

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

Back

If two lines are coincident, they lie on top of each other and have infinitely many solutions.