Graphing Systems of Equations

Front

What is a system of equations?

Back

A group of two or more equations that have the same variables and a solution that makes all equations true.

Front

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

Back

It means to graph each equation on the same coordinate plane and identify the point(s) where the lines intersect, which represents the solution.

Front

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

Back

(1, 3)

Front

What is the graphical representation of the equation y = 3x + 2?

Back

A straight line with a slope of 3 and a y-intercept of 2.

Front

How do you determine if a system of equations has no solution?

Back

If the lines are parallel and never intersect, the system has no solution.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

It means the equations represent the same line, and every point on that line is a solution.

Front

What is the slope of the line represented by the equation y = -2x + 5?

Back

-2

Front

How can you find the x-intercept of the equation y = 4x - 8?

Back

Set y to 0 and solve for x: 0 = 4x - 8, so x = 2.

Front

What is the y-intercept of the equation y = 5x + 3?

Back

3

Front

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

Back

(1, 3)