4-5: Solving Systems of Equations by Graphing

Front

What is the solution to a system of equations?

Back

Any ordered pair that makes both equations true.

Front

Where do the graphs of two equations intersect?

Back

At the solution (x, y) of the system of equations.

Front

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

Back

(1, 5)

Front

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

Back

There is no solution to the system.

Front

What does it mean if two lines coincide in a system of equations?

Back

There are infinitely many solutions to the system.

Front

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

Back

(2, 4)

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

If a system of equations has one solution, what does that indicate about the lines?

Back

The lines intersect at exactly one point.

Front

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

Back

(1, 3)

Front

What is the significance of the slope in a linear equation?

Back

It represents the rate of change of y with respect to x.