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 a solution?

Back

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a system of equations?

Back

The lines representing the equations are graphed 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 does it mean if two lines are parallel?

Back

The system of equations has no solution because the lines never intersect.

Front

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

Back

(1, 3) - The lines intersect at this point.

Front

What is the significance of the point (0,0) in a system of equations?

Back

It is the origin and can be a solution if it satisfies the equations.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the x-intercept of a linear equation?

Back

Set y = 0 and solve for x.