The graphs with equations and meet at two points. At one of these points, . What is the value of at the other point?
I dont know how to do this question, I think i should set them equal to each other,
any help appreciated.
I recommend substituting for y as given by the first equation into the second equation. This will given you a quadratic in x. Solve this, then plug the root not equal to 2 into the first equation for x to determine the value of y at the other point.
If you substitute for y using the first equation, into the second equation, you get:
$\displaystyle x\left(\frac{9}{4}x-4 \right)=1$
Distribute the x on the left side:
$\displaystyle \frac{9}{4}x^2-4x=1$
Multiply through by 4:
$\displaystyle 9x^2-16x=4$
Write quadratic in standard form:
$\displaystyle 9x^2-16x-4=0$
Now factor to find the roots.