Question 123337
Given the two equations:
.
{{{x - 3y = 0}}} and
.
{{{x*y = 27}}}
.
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:
.
{{{y = 27/x}}}
.
Now you can go to the first equation and replace y by its equal which is {{{27/x}}}. When
you make that replacement in the first equation it becomes:
.
{{{x - 3*(27/x) = 0}}}
.
Multiply the -3 times the numerator 27 and this equation then is:
.
{{{x -81/x = 0}}}
.
You can next get rid of the denominator of x by multiplying both sides of the equation (all terms)
by x to get:
.
{{{x^2 - 81 = 0}}}
.
Get rid of the -81 on the left side by adding +81 to both sides to get:
.
{{{x^2 = 81}}}
.
Take the square root of both sides and you have two answers:
.
{{{x = 9}}} and {{{x = -9}}}
.
So there are also two possible answers for y. Recall that we had {{{y = 27/x}}}. This means that
when x = +9 the corresponding value of y is {{{y = 27/9 = 3}}}.
.
And when x = -9 the corresponding value of y is {{{y = 27/-9 = -3}}}
.
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.
.