Solve using elimination, substitution or by graphing. Click question to see the system!

Question

X² + y = 8

e^x - y = 0

Answer 1

This seemed pretty difficult to solve algebraically with the exponential function, so I chose to solve by graphing. I solved both for y

y=8-x²

y=e^x

I graphed them on the TI-84 and use the intersection feature to solve. They intersect at

(-2.818, 0.060)

(1.658, 5.250)

(Rounded to 3 decimals)

Answer 2

You can also try to convert e^x into a power series, up to a quadratic: e^x = 1 + x + x/2! ...

This way you have an equation as below:

3/2 X² + X - 7 = 0

Solve it and you got X₁ = 1.85 and X₂ = - 2.52. You can go with a cubic equation to get more accurate values.

However, I think there should be an analytic solution as well.