Verified Answer :

luana

\(\left \{ {{15x-12y=13\ \ | multiply\ by\ -2} \atop {30x+9y=4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }} \right. \\\\ \left \{ {{-30x+24y=-26} \atop {30x+9y=4}} \right.\\addition\ method\\\\33y=-22\ \ \ \ | divide\ by\ 33\\\\ y=-\frac{22}{33}\\\\ 15x=13+12y\\\\ x=\frac{13+12y}{15}=\frac{13+12*(-\frac{22}{33})}{15}=\frac{13-\frac{264}{33}}{15}=\frac{13-8}{15}=\frac{1}{3}\\\\ Solution \ is\ x=\frac{1}{3}.\)

apologiabiology

so assuming that x and y are the same value in both equations we can make the first equation negative (multiply the whole thing by -1) and get

-15x+12y=-13
we multiply it by 2 and get
-30x+24y=-26
we add this to the second equation
(30x+9y=4)+(-30x+24y=-26)
30x-30x+24y+9y=-22
or 33y=-22
divide both sides by 11
3y=-2
divide both sides by 3
y=-2/3

we subtitute it into the first equation
15x-12(-2/3)=13
15x-(-24/3)=13
15x+8=13
subtract 8 from both sides
15x=5
divide both sides by 5
3x=1
divide both sides by 3
x=1/3

so x=1/3
y=-2/3

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