Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 170032: Hi, Can you please help?
.
When given the system of equations of
 system (3x-5y=11,8x+7y=9)
.
If you are solving it using elimination
.
This is how I would solve it
.
I would multiply the whole second equation by  5/7
.
 8x+7y=9 =  (5/7)(8x+7y)=(5/7)9 =  (40/7)x+5y=45/7
.
I would then add this equation with the first equation
.
 system( 3x - 5y = 11, (40/7)x+5y=45/7)
.
I would then come up with  (61/7)x = 122/7 , then I solve it, and find that "x" = 2, then I would plug in the answer, and find that "y" = (-1)
.
Is this how elimination works?
.
Or do you have to do it this way...
.
 system (3x-5y=11,8x+7y=9)
.
Multiply the first equation by "7" and the second by "5"
.
I did the math and came up with
.
 system (21x-35y=77,40x+35y=45)
.
Then add the equations
.
I get  61x = 122 , and then find "x" is "2", and "y" = (-1)
.
I will be doing quizzes soon, and I perfer the first way, but does elimination mean you do it the second way
.
What I am asking is, is it o.k. to do elimination the first way, or is the second way, the right way to do it?
.
Thanks ahead of time, Levi
: Hi, Can you please help?
.
When given the system of equations of
 system (3x-5y=11,8x+7y=9)
.
If you are solving it using elimination
.
This is how I would solve it
.
I would multiply the whole second equation by  5/7
.
 8x+7y=9 =  (5/7)(8x+7y)=(5/7)9 =  (40/7)x+5y=45/7
.
I would then add this equation with the first equation
.
 system( 3x - 5y = 11, (40/7)x+5y=45/7)
.
I would then come up with  (61/7)x = 122/7 , then I solve it, and find that "x" = 2, then I would plug in the answer, and find that "y" = (-1)
.
Is this how elimination works?
.
Or do you have to do it this way...
.
 system (3x-5y=11,8x+7y=9)
.
Multiply the first equation by "7" and the second by "5"
.
I did the math and came up with
.
 system (21x-35y=77,40x+35y=45)
.
Then add the equations
.
I get  61x = 122 , and then find "x" is "2", and "y" = (-1)
.
I will be doing quizzes soon, and I perfer the first way, but does elimination mean you do it the second way
.
What I am asking is, is it o.k. to do elimination the first way, or is the second way, the right way to do it?
.
Thanks ahead of time, Levi

Answer by checkley77(3848) About Me  (Show Source):
You can put this solution on YOUR website!
IF BOTH MATHODS GETS YOU THE CORRECT ANSWERS THEN YOU SHOULD CHOOSE THE SHORTEST METHOD. LESS CHANCE OF MAKING A MISTAKE IN THE MATH & YOU'RE USING WHOLE NUMBERS RATHER THAN FRACTIONS (WHICH CAN GET MESSY OR CONFUSING).