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Sedaia [141]
2 years ago
5

1/3 x− 1/8 y=3 7y+9x=−2 please solve the system 45 points for who does

Mathematics
1 answer:
photoshop1234 [79]2 years ago
7 0

Answer:

x=6\\y=-8

Step-by-step explanation:

\frac{1}{3}x-\frac{1}{8}y=3\\ 7y+9x=-2

One method could be rewriting the second equation as x in terms of y and solving by replacing in the first equation.

7y+9x=-2\\9x=-2-7y\\x=\frac{-7y-2}{9}

Replace...

\frac{1}{3}x-\frac{1}{8}y=3

\frac{1}{3}(\frac{-7y-2}{9})-\frac{1}{8}y=3

\frac{-7y-2}{27}-\frac{1}{8}y=3

-\frac{7}{27}y-\frac{2}{27}-\frac{1}{8}y=3

add \frac{2}{27} on both sides.

-\frac{7}{27}y-\frac{1}{8}y=3+\frac{2}{27}

Combine like terms

\frac{(-7)(8)-(1)(27)}{(27)(8)} y=\frac{(3)(27)+2}{27}

\frac{-56-27}{216} y=\frac{81+2}{27}

\frac{-83}{216}y =\frac{83}{27}

Now, to get rid of the fraction and isolate y, multiply by the reciprocal or the inverted fraction.

(\frac{216}{-83}) \frac{-83}{216}y =\frac{83}{27}(\frac{216}{-83})

y=\frac{216}{-27}

Simplify

y=-8

Now replace the value of y in either equation to find x.

7y+9x=-2\\7(-8)+9x=-2\\-56+9x=-2

add 56

56-56+9x=-2+56\\9x=54\\

Divide by 9

\frac{9x}{9}=\frac{54}{9}\\  x=6

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.

\frac{1}{3}x-\frac{1}{8}y=3

\frac{1}{3}(6)-\frac{1}{8}(-8)=3

2-(-1)=3\\2+1=3\\3=3

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

7y+9x=-2\\7(-8)+9(6)=-2\\-56+54=-2\\-2=-2

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