Here's your problem:

y=2x-5
y=7x

1. Graph each line using the slope-intercept method (shown at right).
2. Find the point of intersection of the two lines. (If you are doing this on a graphing calculator, press 2nd, Trace, 5(intersection), and then enter 3 times.
The point of intersection in this problem is (-1,-7).
3. The point of intersection is your solution. You did it!

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Here's the next problem:

The drama club sold 1500 tickets for the end-of-year performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $16,200. How many students attended the play?

1. Write two separate equations. Let x equal the number of adults and let y equal the number of students.

12x+6y=16200
x+y=1500

2. Eliminate one of the variables by multiplying one or both equations by a number that will make one variable cancel out the other in the equations by giving them the same coefficient and a different sign.

12x+6y=16200
-12(x+y=1500)

After you do this you get:

12x+6y=16200
-12x-12y=-18000

The "x's" cancel out to give you:

6y=16200
-12y=-1800

3. Add the equations to get:

-6y=-1800

4. Divide both sides by -6:

y=300

This means that 300 students attended the play. Congratulations! You're done!

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Heres the problem:

3x+4y=-4
x+2y=2

1. Solve one of the equations for one of its variables.

Let's solve the second equation for x. Subtract both sides by 2y to give you:

x=-2y+2

2. Plug the answer you got for x into the first equation:

3(-2y+2)+4y=-4

3. Now solve for y.

Distribute the 3 to everything in the parenthesis:

-6y+6+4y=-4

Add the "y's" together to get:

-2y+6=-4

Subtract 6 from both sides:

-2y=-10

Divide both sides by -2 to get the value of y:

y=5

4. Plug the value of y into the original second equation:

x+2(5)=2
So x+10=2

Now subtract both sides by 10 to give you the value of x:

x=-8

5. Your answer will be an ordered pair. In this case, the solution is (-8,5).

You did it!!!

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