SOLUTION: solving by addition method: 9x+9=7y 5x+3y=-19 doI reverse the equation I am confused

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Question 171884: solving by addition method: 9x+9=7y
5x+3y=-19 doI reverse the equation I am confused
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9x%2B9=7y Start with the first equation


9x=7y-9 Subtract 9 from both sides.


9x-7y=-9 Subtract 7y from both sides.



So we have the system of equations:


system%289x-7y=-9%2C5x%2B3y=-19%29


-5%289x-7y%29=-5%28-9%29 Multiply the both sides of the first equation by -5.


-45x%2B35y=45 Distribute and multiply.


9%285x%2B3y%29=9%28-19%29 Multiply the both sides of the second equation by 9.


45x%2B27y=-171 Distribute and multiply.


So we have the new system of equations:
system%28-45x%2B35y=45%2C45x%2B27y=-171%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-45x%2B35y%29%2B%2845x%2B27y%29=%2845%29%2B%28-171%29


%28-45x%2B45x%29%2B%2835y%2B27y%29=45%2B-171 Group like terms.


0x%2B62y=-126 Combine like terms. Notice how the x terms cancel out.


62y=-126 Simplify.


y=%28-126%29%2F%2862%29 Divide both sides by 62 to isolate y.


y=-63%2F31 Reduce.


------------------------------------------------------------------


-45x%2B35y=45 Now go back to the first equation.


-45x%2B35%28-63%2F31%29=45 Plug in y=-63%2F31.


-45x-2205%2F31=45 Multiply.


31%28-45x-2205%2Fcross%2831%29%29=31%2845%29 Multiply both sides by the LCD 31 to clear any fractions.


-1395x-2205=1395 Distribute and multiply.


-1395x=1395%2B2205 Add 2205 to both sides.


-1395x=3600 Combine like terms.


x=%283600%29%2F%28-1395%29 Divide both sides by -2205 to isolate x.


x=-80%2F31 Reduce.


So our answer is x=-80%2F31 and y=-63%2F31.


Which form the ordered pair .


This means that the system is consistent and independent.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
solving by addition or subtraction is the same as the elimination method..The purpose is to arrange and manipulate the equations so that one of the variables is eliminated...and once that takes place you can easily solve for the variable that is remaining......once that takes place you can then take you found value and plug it back into either original equation to solve for the variable that was eliminated. It is much easier to do this if like terms are lined up when obseving in a vertical manner. I changed eq 1 from 9x+9=7y to 9x+7y=9....I think you copied it wrong because I was getting some very strange numbers.
:
9x+7y=9......eq 1
5x+3y=-19.....eq 2
:
The key is to look at both variables to figure which one will require the least amount of manipulation. Many times its all set up and you will have a y and -y or a x and -x in either equation. This problem will require us to multiply bothe equations. You can either multiply all terms in eq 1 by -5 and all terms in eq 2 by 9 in order to eliminate the x terms or you can multiply all the terms in eq 1 by 3 and all the terms in eq 2 by -7 to get rid of the y terms. I choose the latter.
:
3(9x+7y=9)-------->27x+21y=27
-7(5x+3y=-19)---->-35x-21y=133........now you can see when they are lined up
.....................................that if you add the two eq. the y terms
.....................................are elimiated because -21y+21y=0
:
we are left with 27x-35x=27+133
:
now we combine like terms isolating the x term -8x=160...dividing by -8:
highlight%28x=-20%29
:
now plug this value into eq 1 or eq 2. I choose eq 2.
:
5(-20)+3y=-19
:
-100+3y=-19
:
-3y=81
:
highlight%28y=-27%29