Coordinate geometry
Which of the following is the y-coordinate of the point of intersection of lines:y=ax+1/b and y=bx+1/a? (Given a is not equal to b)
a) 1
b) 2
c) 3
d) 6
I tried setting these up as simultaneous equations:
y = ax + 1 / b -> by = abx + 1 -> abx - by = -1
y = bx + 1 / a -> ay = abx + 1 -> abx - ay = -1
Now, subtracting the second one from the first one, I get:
abx - by = -1
-abx + ay = 1
Adding them together, I get:
(a - b)y = 0
This means either:
y = 0 -> not one of the above choices
or
a - b = 0 -> a = b -> which is contrary to the instructions for the problem (Given a is not equal to b)
Are you sure you have stated everything correctly?
Yeah , I am 100% sure
Then I must be doing something wrong that I didn't discover even looking over it a second time. Incidentally, I edited my response to show that I subtracted the second one from the first (I had originally written that I had subtracted the first one from the second even though I had done the opposite), plus I showed the x terms in the intermediate results.
Maybe someone else here can see the way to the proper solution. Or if this was given to you by a teacher, see if this person knows what to do.
May be option of answer is wrong?
Do you mean that 0 should have been one of the choices? I think it should have been.
OR, 1 is near to zero rather than other . so a is answer
Here's another question.
If the circle is translated three units to the up and three units to the right and the radius increased by 2 units , what will be the equation of the circle?
a) x^2+(y-7)^2=36
b) (x-7)^2+(y-4)^2=36
c) (x-7)^2+y^2=100
d) (x+1)^2+y^2=100
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