APRIL'S
AWESOME ALGEBRA
| The purpose for this page is to show you how to solve systems of equations. The 2 ways I will show you are solving by substitution and elimination. Also I will show you how to solve a linear word problem, so....here we go! | 
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| Solving by
substitution:
2x + y = -6 2x + y = -6 2(
- 4 ) + y = -6 |
First, you look at you two equations and decide witch one is easiest to
put in y equals form. I chose the top equation. Once in the y equals form
you can simply insert it in the place of y in the second equation. Then
you combine all the variables ( 3x and -2x). Then you should be left with
a variable (there may be a muber attached) and there might also be a single
number (-6). In order to get rid of the single number you must take it to
the other side. By doing that you must change the sign ( if it is positive
it becomes negative and if it is negative it becomes positive), ( -6 taken
to the other side is 6 and it is taken from - 10) and then you can see that
x = -4. The last part is so easy. You simply take the x = -4 and put it inthe
the place of x in the second equation (or the one that you did not solve
first). When you end the equation then you have and x and a y.
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Solving by linear combination...
5x - 2y = 4 5x - 2y = 4 5x +
6x = 11x
11x + 0 = 22 5(2)
-2y = 4
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To solve a problem like this you must
first look at the x and y. In order to combine the two equations you must
make either the x or the y 'cancel out' (or die as Mrs. Felz would say).
So for this problem I mutiplied the bottom equation times 2 so that the negative
2 in the first equation would cancel with the new 2 y in the bottom equation.
Then you take the two equations and add them together. Then you take the
x and plug it into one of the equations to find y. When you have the y then
you have the answer. 
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| solving
word problems...
the sum of a certain number and a second number is -42. The first number minus the second is 52. Find the numbers. x + y = -42 2x = 10 5 + y = -42 -42 - 5 = -47 x = 5 |
First of all you make two equations from the world problem. You use either
way (of solutions) to solve for x and y in the equations. This problem I
used linear combination. The y cancels and leaves you with a problem to solve
for x. When you get x you stick x in place of an x in the equation (either
one). Then you have the answer for x and y. You can put them both in place
and check to make sure that the answer is correct. 
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