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3 votes
1/2x + 1/3y = 0

1/4x -1/2 y = 8
What is the solution of the system shown?
(-8, 12)
(8, -12)
(8, 12)

2 Answers

2 votes

Answer:

(8,-12) the second option :)

Explanation:

User Dyomas
by
8.7k points
6 votes

Answer:


(8,-12)


Explanation:

The two equations are:


(1)/(2)x+(1)/(3)y=0\\(1)/(4)x-(1)/(2)y=8


We can solve the first equation for
x and then substitute into second equation to find the value of
y.


(1)/(2)x+(1)/(3)y=0\\(1)/(2)x=-(1)/(3)y\\x=(-(1)/(3)y)/((1)/(2))\\x=-(2)/(3)y

Now,


(1)/(4)x-(1)/(2)y=8\\(1)/(4)(-(2)/(3)y)-(1)/(2)y=8\\-(2)/(12)y-(1)/(2)y=8\\-(2)/(3)y=8\\y=(8)/(-(2)/(3))\\y=-12


Substituting
y=-12 into the "solved for
x" version of first equation, we get the value of
x. So,


x=-(2)/(3)y\\x=-(2)/(3)(-12)\\x=8


Hence the ordered pair is
(8,-12) and this is the solution to the system of equations shown.

User Marius Kaunietis
by
8.1k points

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