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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does it mean if a system of equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, so every point on the line is a solution.

Front

How do you graph the equation y = mx + b?

Back

Start at the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

Front

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

Back

The slope is 1/2.

Front

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

Back

The y-intercept is 9.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines: parallel lines (no solution), same line (infinitely many solutions), or intersecting lines (one solution).

Front

Solve the system of equations by graphing: y = 1/2x + 2 and y = -3x + 9. What is the solution?

Back

(2, 3)