Solving Systems of Equations by 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 a system of equations to have infinite solutions?

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

What is the graphical representation of intersecting lines?

Back

Intersecting lines cross at one point, which represents the unique solution to the system.

Front

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

Back

(1, 3) is the solution where the two lines intersect.

Front

What does the graph of parallel lines look like?

Back

Parallel lines are equidistant from each other and never meet, indicating no solution.

Front

If two lines intersect at (4, -2), what does this point represent?

Back

This point represents the solution to the system of equations.

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) indicates the steepness and direction of the line.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis.