Question 1086817
the solution is selection b. (2.07,1.38)


you can solve it algebraically as follows:


start with:


25x^2 – 4y^2 = 100
36y^2 – x^2 = 64


re-arrange the terms so that they line up like for like.


25x^2 - 4y^2 = 100
-x^2 + 36y^2 = 64


multiply both sides of the second equation by 25 to get:


25x^2 - 4y^2 = 100
-25x^2 + 900y^2 = 1600


add the equations together to get:


896y^2 = 1700


solve for y^2 to get:


y^2 = 1.897321429


solve for y to get:


y = plus or minus 1.377432913


since the intersection point has to be in the first quadrant, then you get:


y = plus 1.377432913


replace y^2 with 1.897321429 in the first equation to get:


25x^2 - 4 * 1.897321429 = 100


simplify this to get:


25x^2 - 7.589285714 = 100


add 7.589285714 to both sides of the equation to get:


25x^2 = 107.5892857


solve for x^2 to get:


x^2 = 107.5892857/25 = 4.303571429


solve for x to get:


x = plus or minus 2.074505104.


since x has to be in the first quadrant, then you get:


x = plus 2.074505104.


your intersection point in the first quadrant is:


(x,y) = (2.074505104,1.377432913)


round this to 2 decimal digits and you get:


(x,y) = (2.07,1.38)


that's selection b.


graphically, this looks like this:


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