1. ## line meeting curve.

hi agian!

how do you fine the coorrdinates where the line $\displaystyle 2x+3y=1$ meets the curve $\displaystyle x(x-y) = 2$

kind regards

hi agian!

how do you fine the coorrdinates where the line $\displaystyle 2x+3y=1$ meets the curve $\displaystyle x(x-y) = 2$

kind regards

Solve $\displaystyle 2x+3y=1$ for y, plug this y value into $\displaystyle x(x-y) = 2$, and solve the resulting equation for x. The use these x values in either of the original equations to get the corresponding y values. I got (6/5, -7/15) and (-1, 1).

-Dan

hi agian!

how do you fine the coorrdinates where the line $\displaystyle 2x+3y=1$ meets the curve $\displaystyle x(x-y) = 2$

kind regards

Rewrite the first equation as

$\displaystyle y=\frac{1-2x}{3}$

Then substitute this for $\displaystyle y$ in the second equation:

$\displaystyle x(x-\frac{1-2x}{3}) = 2$

and solve for $\displaystyle x$.

Then substitute the value/s of $\displaystyle x$ that you have
found back into one of the equations and solve for $\displaystyle y$.

RonL

4. thanks captainblack!

5. ## re:

$\displaystyle x(x-\frac{1-2x}{3}) = 2$

$\displaystyle x(x-\frac{1-2x}{3}) = 2$

$\displaystyle x(x-\frac{1-2x}{3})=\frac{x(3x-1+2x)}{3}=\frac{5x^2-x}{3} = 2$

which simplifies to:

$\displaystyle 5x^2-x - 6=0$

which is a quadratic which you can solve using the quadratic formula.

RonL