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 for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How do you determine if a point (x, y) is a solution to the system?

Back

Substitute x and y into each equation; if both equations are true, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect on a graph?

Back

The intersection point represents the solution to the system of equations.

Front

What is the y-intercept of a line?

Back

The y-coordinate where the line crosses the y-axis (x=0).

Front

How can you find the y-intercept from an equation in slope-intercept form?

Back

In the equation y = mx + b, b is the y-intercept.

Front

What is slope in the context of a linear equation?

Back

Slope (m) represents the rate of change of y with respect to x.

Front

What does it mean if two lines are parallel?

Back

They have the same slope and will never intersect, indicating no solution to the system.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, indicating infinitely many solutions.