Welcome to the equations and graphing Algebra 2 Tutorial!

You can determine whether a given point is a solution to a system by plugging a given set of points into the two given equations. If the equation makes sense with a given set of points, then it is a solution.

Check whether (0,3) is a solution to the following system.

5x + 3y = 6 --> 5(0) + 2(3) = 6  

Since (0,3) is a solution to this equation, it is a solution to the system.

If the two equations intersect at one point, then it has exactly one solution.

If each point on the line is a solution, then it has infinitely many solutions.

If the two lines have no point of intersection, then the system has no solution.

x + y = 3 --> y = - x + 3

2x - 4y = 4 --> - 4y = - 2x + 4, y = 1/2x - 1

Here you solve the system of two equations by graphing the equations by hand.

Practice Problems:

Check whether (3,7) and (4,5) are solutions to the following systems.

5x + 3y = 0

6x + 7y = 4

Determine how many solutions the following linear systems have by graphing.

1) 2x - y = 4

   - 6x + 3y = -18

2) 6x - 2y = -2

    -3x -7y = 17

3) 21x- 7y = 7

    -3x + y = -1

Graph this system of two equations by graphing the equations by hand.

3x + 2y = 2

4x + 8y = 3