Solving Systems of Equations by Graphing (y=mx+b form)

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 the slope-intercept form of a line look like?

Back

The slope-intercept form of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope (m) from an equation in slope-intercept form?

Back

The slope (m) is the coefficient of x in the equation y = mx + b.

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Front

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

Back

1. Start at the y-intercept (0, b). 2. Use the slope (rise/run) to find another point. 3. Draw a line through the points.

Front

What is the solution to a system of equations graphically?

Back

The solution is the point where the graphs of the equations intersect.

Front

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

Back

If two lines are parallel, they have the same slope but different y-intercepts, meaning they have no solution.

Front

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

Back

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

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

1. One solution: lines intersect at one point. 2. No solution: lines are parallel. 3. Infinitely many solutions: lines are coincident.

Front

Solve the system of equations by graphing: y = -2/3x + 4 and y = -1/3x + 1.

Back

The solution is (9, -2).