Solving systems of equations

".....mellow is the man who knows what he's been missing. Many, many men can't see the open road. Many is a word that only leaves you guessing. Guessing 'bout a thing you really ought to know. You really ought to know." -Over the Hills and Far Away - LED ZEPPELIN

LINEAR COMBINATION----> ---->

Problems: -3x + 2y = -6

5x + 2y =18

The first step in solving these equations is to mulitiply equation two by negative one so that the y factors will cancel out. That gives you -8x = -24.
Now, that makes x = 3. Substituting into the first equation we get -3(3) + 2y = -6. This becomes
-9 + 2y = -6. So, 2y = 3 and y = 1.5.

The solution is (3, 1.5).

Problems: 4x + 8y = 17

x + 4y = 8

When solving an equation by substitution the first step is to solve for either the x or y variable in equation 2. You get this answer by subtracting 4y from each side. Then you get x=8-4y for equation two which you substitute into equation one.

This gives us 4(8-4y) + 8y = 17.
Then distribute the 4 to get 32 - 16y +8y = 17.
Then combine like terms to get 32 -8y = 17
The next step is to subtract 32 from each side to get -8y = - 15.
Then, divide both sides by negative eight to get y = 15/8
Finally, substitute this into the problem for y to get
x + 4(15/8) = 8. You should then solve for x to get 1/2. You can then state these answers as a point like (1/2, 15/8).

<---- <---- SUBSTITUTION

GRAPHING ----> ---->

Problems: -7x-y = -10

3x + 4y = -10

The first step in this problem is to get both equations to their y-intercept form. (Your results should look like this: Y = -7x + 10 and Y = 3/4x - 10/4)

Next, you should enter these results into your graphing calculator or you can do them by hand.

Finally, you should calculate the intersection at which the lines meet. For these equations you should get x = 2 and y = -4. In point form these numbers should look like ( 2,- 4).