Question 114737
1.
Solve by elimination: 

{{{(1/3)x+2/1=2/1}}}………………...(1)……multiply both sides by {{{3}}}

{{{(2/3)x-(3/5)y=1/5}}}………………...(2) ……multiply both sides by {{{3}}}


{{{(1/3)3x + 3*2/1 = 3*2/1}}}………………...(1) 

{{{(2/3)3x - (3/5)3y = 3*1/5}}}………………...(2) 


{{{x + 6=  6}}}………………...(1) ……..… multiply both sides by {{{2}}}

{{{2x - (9/5)y = 3/5}}}………………...(2) 


{{{2x + 12 =  12}}}………………...(1)… subtract (2) from (1)

{{{2x - (9/5)y = 3/5}}}………………...(2)

 
{{{2x + 12 =  12}}}………………...(1)

-{{{2x - (9/5)y = 3/5}}}………………...(2)
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{{{2x-2x+12-(-(9/5)y) = 12 – 3/5}}}


{{{12 +(9/5)y = 12 –3/5}}}….move {{{12}}} from the left to the right


{{{(9/5)y = 12 -(12+3/5)}}}


{{{(9/5)y = -(3/5)}}}.......divide {{{-3/5}}} by {{{9/5}}}


{{{y = -(3/5)/(9/5)}}}.......simplify


{{{y = -(3*5)/(9*5)}}}.......


{{{y = -1/3}}}.......


2.

Solve by elimination:

{{{x-y=-13}}}………………...(1) ……..… multiply both sides by {{{9}}}
{{{9x-4y=-97}}}………………...(2)

 {{{9x - 9y = -117}}}………………...(1) …. subtract (2) from (1)
-{{{9x-4y=-97}}}………………...(2)
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{{{9x – 9x + y – (-4y) = - 117 – (-97)}}}

{{{ y + 4y = - 117 + 97}}}

{{{ 5y = -20}}}

{{{ 5y = -20}}} …………….divide both sides by {{{5}}}

{{{ (5/5)y = -(20/5)}}}


{{{ y = - 4}}}


3.

Solve by substitution:

{{{x+y=7}}}………………...(1)……… substitute (2) in (1)
{{{y=x-1}}}…………………(2)

{{{x + (x-1) = 7}}}………………...(1)………
{{{x + x-1 = 7}}}………………...(1)………
{{{2x -1 = 7}}}………………...(1)……… move {{{-1}}} from the left to the right
{{{2x = 7 + 1}}}………………...(1)………

{{{2x = 8}}}………………...(1)……… divide both sides by {{{2}}}

{{{(2/2)x = 8/2}}}………………...(1)………

{{{x =  4}}}………………...(1)……… now substitute {{{x =  4}}} in (2)


{{{y= x-1}}}…………………(2)
{{{y= 4-1}}}…………………(2)
{{{y= 3}}}…………………(2)

So, your solution is:

{{{x =  4}}} and {{{y= 3}}}