Mathematics

Problem

65. An Ellipse and a Line Consider the system of equations

\begin{aligned} \frac{x^{2}}{4}+\frac{y^{2}}{9} & =1 \\ x+y & =1 \end{aligned}

(a) Solve the equation

x^{2} / 4+y^{2} / 9=1

for

y

in terms of

x

to determine the two implicit functions determined by the equation. (b) Solve the system of equations graphically. (c) Use substitution to confirm the solutions found in part (b).

Browse the problem library