$\begingroup$

So i have the following equations:

$x=3-4t$,

$y=5+2t$

I'm slightly puzzled by this. The question asks to find $x$ in terms of $y$, but the above equations have also $t$ included. This to me signals that I need to preprocess the equations such that the $t$ variable is cancelled out entirely. This can ofcourse be easily done with elimination. However, that would result in a single equation with two unknow variables $x$ and $y$ which would be impossible to evaluate as it would just give me an expression. What should I do in this case?

$\endgroup$ 1

3 Answers

$\begingroup$

By equation 2$$y=5+2t\\ t=\frac{y-5}{2}\\ $$substitute this equation into equation 1$$ x=3-4\frac{y-5}{2}\\ x=13-2y $$

Finally we get $x=13-2y$

$\endgroup$ $\begingroup$

Add equation $(1)$ with two times equation $(2)$, you get$$2y+x = 13$$

$\endgroup$ $\begingroup$

From the second equation, $t=(y-5)/2.$ Now substitute this expression for $t$ in the first equation.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy