Last Step of a Parametric to Cartesian Conversion

Question

I need to figure out how to combine the (4) line to make the t=y-z/R+x and I just don't have any ideas. I'm sorry if these seem basic but I'm 16 and struggling through a topic I've never done before.

Thanks in advance.

Answer 1

Just add the two equations together: $$2(z+Rt)+2tx=y(1+t^2)+y(1-t^2)$$ Simplify both sides: $$2z+2Rt+2tx=2y$$ Divide both sides by $2$: $$z+Rt+tx=y$$ Subtract both sides by $z$: $$Rt+tx=y-z$$ Factor out a $t$ from the left side: $$t(R+x)=y-z$$ Divide both sides by $R+x$: $$t=\frac{y-z}{R+x}$$