To see if a given coordinate is a solution of a System of Linear Equations you just take
the x point and plug it into the x in the equation and take the y point and plug it into the
y in the equation. If the the solution is satisfied than the points are a solution of the
equation.

Example: Is (3,2) a solution of

6x+4y=26
2x+3y=12

The point (3,2) is a soluiton of the Systems of Linear Equations because the two equations
are true with this point.

Now, lets use the same equations but use the point (3,6) is this a solution to the systems of
equations.

6x+4y=26
2x+3y=12

This point is not a solution to this system of equations because in the first equation with the
points plugged in the solution is 42, and the solution to the second equation is 24. As you
can see these values are now where near the values of the two systems of equation above.

Solving a System Graphically

Lets use these equations: 2x - 3y = 1   and x + y = 3

One of the easiest ways to find the solution is to graph these and see where they intersect.
To do this, simply put each into slope-intersect form ( y = mx + b). Lets do this.......

2x - 3y = 1 turns into y = 2/3x - 1/3  

x + y = 3 turns into y = -x + 3   

Now view the graph at the side

It may not be as clear on my graph, but the point of intersection is (2,1). In cases where
this is not clear, you can always refer to your Texas Instrument, preferably a higher numbered
one. Here are the steps:

Click the Y= buttons in the upper left hand corner. Type in your equations in the slope intercept
form. use the X,T,O,n   button for your x. After you have typed these in, click the graph button.
You will see your lines on the screen. Next, do 2nd and Trace. The CALCULATE screen will be
brought up. Use function 5, intersect. You will be brought back to the screen. Simply click the
enter button 3 TIMES and your x and y coordinates will be put in bottom of the screen. If you
do not see these or encounter problems, try adjusting your window so that the point of intersection
is on the screen.

Now that we have seen how to do these equations by graphing, lets try a few on our own. The
answers will be posted below.

Directions: Check whether the ordered pair is a solution of the system

1. (6, -1)

4x - y = 25

-3x - 2y = -16

2. (3,0)

-x + 2y = 3

10x + y = 30

Correct Answers:
1. Yes
2. No