60d1b6a5-bd62-46b4-a514-3f1ec6c8775b 27 overlord 4 5 false false 0 decimal

&[DATE] &[TIME]

eq.1 x 2 ^ y * y 2 ^ x * + 1 + : eq.2 x 2 ^ y + 3 - : 2 1 sys

As you can see two equation intersect at five points. So there are five solutions for these two equations. Integrated solve() function shouldn't accept multiple equations as far as I know, it is for single equation solution. roots() and FindRoot() can solve this type of problems but they will give you single solution for designated range. It is better to plot equations, determine the range by intersections and try to find all solutions either by roots() or FindRoot() by changing the ranges.

FindRoot() needs guesses as starting point. It can assign to variable if guess is written as a boolean equation. However this is not a dependable way as solution changes if order of unknows change in list.
roots() sometimes doesn't need guess. But you have to enter ranges to find a single or all solutions in some occasions as shown this example.

eq.1 0 ≡ eq.2 0 ≡ 21 mat x y 21 mat 3 - 1 - 21 mat roots 1.8074 - 0.2667 - 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat 3 - 121 mat FindRoot 1.8074 - 0.2667 - 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat x y 21 mat 1 - 221 mat roots 1.1526 - 1.6716 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat 1 - 121 mat FindRoot 1.1526 - 1.6716 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat x y 21 mat 0.1 - 221 mat roots 0.1167 - 2.9864 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat 0.5 - 121 mat FindRoot 0.1167 - 2.9863 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat x y 21 mat 21 - 21 mat roots 1.8363 0.3719 - 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat 21 - 21 mat FindRoot 1.8363 0.3719 - 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat x y 21 mat 33 - 21 mat roots 2.2404 2.0194 - 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat 22 - 21 mat FindRoot 2.2404 2.0194 - 21 mat

eq.1 0 ≡ eq.2 0 ≡ 21 mat x 2 ≡ y 2 - ≡ 21 mat FindRoot 2.2404 2.0194 - 21 mat

x 2.2404

<<<< Solution exist, x and y are correct.

y 2.0194 -

x y Clear 1

eq.1 0 ≡ eq.2 0 ≡ 21 mat y 2 - ≡ x 2 ≡ 21 mat FindRoot 0.1167 - 2.9864 21 mat

x 2.9864

<<<< Solution exist but x and y are swapped.

y 0.1167 -