SOLUTION: x-3y=0 xy=27

Question 123337: x-3y=0
xy=27
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given the two equations:
.
and
.

.
Let's use substitution as a start for solving for x and y. Go to the second equation and
solve for y by dividing both sides of the equation by x to get:
.

.
Now you can go to the first equation and replace y by its equal which is . When
you make that replacement in the first equation it becomes:
.

.
Multiply the -3 times the numerator 27 and this equation then is:
.

.
You can next get rid of the denominator of x by multiplying both sides of the equation (all terms)
by x to get:
.

.
Get rid of the -81 on the left side by adding +81 to both sides to get:
.

.
Take the square root of both sides and you have two answers:
.
and
.
So there are also two possible answers for y. Recall that we had . This means that
when x = +9 the corresponding value of y is .
.
And when x = -9 the corresponding value of y is
.
So the two possible answers to this problem are the pair x = 9 and y = 3 and the pair x = -9 and y = -3.
.
You can validate these two sets of answers by returning to the original equations and
convincing yourself that by substituting +9 for x and +3 for y will make both equations true
and then by substituting -9 for x and -3 for y both equations will also still balance.
.
Hope this helps you to see your way through the problem.
.

RELATED QUESTIONS
(3x^3y^3)/xy=? x and y equal... (answered by mangopeeler07)

simplify: (x^3y^3) (2^0... (answered by stanbon)

Find numerical values for all simultaneous solutions of: X^2+3y^2=27 xy=6 and... (answered by robertb)

Factor the four term polynomial by grouping 1.) x^3+3x^2+9x+27 2.)... (answered by jim_thompson5910)

2x-3y-10=0 and x^2+xy+y^2+2x+y-6=0. Solve... (answered by josgarithmetic)

(2x-3y)/(xy-x^2) (answered by tommyt3rd)

Find the number of ordered triples (x,y,z) of real numbers that satisfy {{{x + y - z = (answered by my_user_id)

x=3y,x-3y=0 (answered by ikleyn,Alan3354)

x+y=7xy, 2x -3y+xy = 0 by both methods elimination and substitution (answered by josgarithmetic)