Answer:
[tex]x=6\\y=-8[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}x-\frac{1}{8}y=3\\ 7y+9x=-2[/tex]
One method could be rewriting the second equation as x in terms of y and solving by replacing in the first equation.
[tex]7y+9x=-2\\9x=-2-7y\\x=\frac{-7y-2}{9}[/tex]
Replace...
[tex]\frac{1}{3}x-\frac{1}{8}y=3[/tex]
[tex]\frac{1}{3}(\frac{-7y-2}{9})-\frac{1}{8}y=3[/tex]
[tex]\frac{-7y-2}{27}-\frac{1}{8}y=3[/tex]
[tex]-\frac{7}{27}y-\frac{2}{27}-\frac{1}{8}y=3[/tex]
add [tex]\frac{2}{27}[/tex] on both sides.
[tex]-\frac{7}{27}y-\frac{1}{8}y=3+\frac{2}{27}[/tex]
Combine like terms
[tex]\frac{(-7)(8)-(1)(27)}{(27)(8)} y=\frac{(3)(27)+2}{27}[/tex]
[tex]\frac{-56-27}{216} y=\frac{81+2}{27}[/tex]
[tex]\frac{-83}{216}y =\frac{83}{27}[/tex]
Now, to get rid of the fraction and isolate y, multiply by the reciprocal or the inverted fraction.
[tex](\frac{216}{-83}) \frac{-83}{216}y =\frac{83}{27}(\frac{216}{-83})[/tex]
[tex]y=\frac{216}{-27}[/tex]
Simplify
[tex]y=-8[/tex]
Now replace the value of y in either equation to find x.
[tex]7y+9x=-2\\7(-8)+9x=-2\\-56+9x=-2[/tex]
add 56
[tex]56-56+9x=-2+56\\9x=54\\[/tex]
Divide by 9
[tex]\frac{9x}{9}=\frac{54}{9}\\ x=6[/tex]
To check whether these values are accurate, replace in either equation both values and you should have an equality. In this case I'll do it in both equations.
[tex]\frac{1}{3}x-\frac{1}{8}y=3[/tex]
[tex]\frac{1}{3}(6)-\frac{1}{8}(-8)=3[/tex]
[tex]2-(-1)=3\\2+1=3\\3=3[/tex]
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[tex]7y+9x=-2\\7(-8)+9(6)=-2\\-56+54=-2\\-2=-2[/tex]
