Math Student Help

I am in 7th grade gifted math learning algebra and am learning how to solve systems by elimination and substitution. I prefer to use elimination so if you could, try to put it in that way. Well, now we have to learn how to solve them with fractions. Like ….

x+16 1/2 = -3/4y
y = 1/2x

How do I solve problems like this?

You need to modify one of the equations so that either the X value or the Y value will cancel out when added to the corresponding X or Y value of the other equation.

Eliminating the Y’s will become a complete mess because of that -3/4 value so lets eliminate the X value instead.

Step 1: swap the 2nd equation so X is on the other side like so
1/2x=y

Step 2: multiply 2nd equation by -2 like so
-2/2x=-2y

-2/2x simplifies to -x

Step 3: Add equation 1 and 2 with one another like so
x+16.5=-3/4y
-x=-2y
0+16.5=-3/4y -2y

Combine -3/4y and -2y together to get -11/4y (-2y is equivalent to -8/4y so -3/4 -8/4 = -11/4)

Step 4: Start Solving for Y in the new equation you just created (we will call this equation #3)
16.5=-11/4y

Lets change 16.5 into the fraction 33/2 (16 1/2 is a sloppy way to write this number in fraction form)

Step 5: Divide both sides by -11/4 so that Y will be by itself. If you are uncomfortable with dividing by fractions then you can first multiply both sides by 4 and then divide both sides by 11. Or you can simply just swap the fraction around and multiply it with what you have on the lefthand side. The SAME answer results from doing this.

I’ll show both steps:
First is just simply swapping 11/4 to 4/11 and multiplying it with 33/2 to get the fraction 132/22. This is not simplified all the way but we will do that later.
Second method is to multiply both sides by 4 which eliminates the "4" on the righthand side and gives us 132/2 on the lefthand side. Now we divide both sides by 11 to get rid of the 11 on the righthand side and gives us 1/11 times 132/2 on the lefthand side. When we multiply those together we get 132/22 which is the same number we got from doing the first method (first method is much quicker, so get comfortable doing it if you can).

132/22 simplifies to 6/1 which is just "6"

Step 6: Write out our Y value answer
Y = 6

Step 7: Substitute "Y=6" into either the first or second equation (but NOT the third equation) to get the x value.

I’ll let you do that part, good luck

This entry was posted on Tuesday, December 22nd, 2009 at 6:32 am and is filed under fractions. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.