Kemal G. answered • 06/01/17
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Hi Youssef,
I will use elimination method to find one of the variables. To do that, I will multiply the second equation by 2.
6x^2-4y^2=36
2*(9x^2+2y^2=90)
2*(9x^2+2y^2=90)
6x^2 - 4y^2 = 36
18x^2 + 4y^2 = 180
18x^2 + 4y^2 = 180
+_________________
24x^2 = 216
x^2 = 9
x = ±3
Now, plug in x = 3 to solve for y.
9x^2 + 2y^2 = 90
9*(3)^2 + 2y^2 = 90
81 + 2y^2 = 90
2y^2 = 9
y^2 = 9/2
y = ±3/√2 = 3√2/2
The solution set is x = {-3, 3} and y = {-3√2/2, 3√2/2}
Kemal G.
Kenneth,
I would appreciate if you provide your own "full solution" and answer instead of making comments to my answers. You did not specify what the ordered pairs represented in your paragraph answer that you provided.
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06/01/17
Kenneth S.
Kemal, my answer showed the path to solution, and included the observation that there are four solutions.
You chose to include more detail, solving for two values of x and for two values of y, with which I have no quarrel.
However, you listed the two x values and the two y values separately, and it's possible that the student would not realize that either x value (positive or negative) can be paired with either y value (+ or-), and thus I pointed this out so that the student would get the four points of intersection.
You need not be thin-skinned!
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06/01/17
Kemal G.
Well, I think it will help more if you convey all this information to the student by providing a full solution. I am thin-skinned because you also made a comment about my other answer (to which I already responded) about the use of asterisk between two numbers being multiplied. I believe that I have enough math background to know this and I stand behind my notation. It feels like you are nitpicking a little bit. I would be happy to get math experts' views on the use of the asterisk sign for multiplying two numbers.
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06/01/17
Kenneth S.
The solution set ought to be given as ordered pairs; there should be four of them, representing the intersection of an ellipse with an hyperbola.
06/01/17