You can put this solution on YOUR website! Given the two equations:
. and
.
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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:
.
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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:
.
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Multiply the -3 times the numerator 27 and this equation then is:
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You can next get rid of the denominator of x by multiplying both sides of the equation (all terms)
by x to get:
.
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Get rid of the -81 on the left side by adding +81 to both sides to get:
.
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Take the square root of both sides and you have two answers:
. and
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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 .
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And when x = -9 the corresponding value of y is
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So the two possible answers to this problem are the pair x = 9 and y = 3 and the pair x = -9 and y = -3.
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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.
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Hope this helps you to see your way through the problem.
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