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 that are solved together.

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.

Front

What is the solution to a system of equations?

Back

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

Front

How do you find the slope of a line from an equation in slope-intercept form (y = mx + b)?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the slope of the line represented by the equation y = -3/2x + 4?

Back

-3/2

Front

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

Back

It means the lines will never intersect, indicating that there is no solution to the system.

Front

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

Back

It means the lines lie on top of each other, indicating that there are infinitely many solutions.

Front

How can you determine the solution to a system of equations graphically?

Back

By identifying the coordinates of the intersection point of the graphed lines.

Front

What is the y-intercept in the equation y = 2x - 1?

Back

-1, which is the point where the line crosses the y-axis.

Front

If a system of equations has no solution, what does that indicate about the lines?

Back

The lines are parallel and will never intersect.