I need help solving simultaneous equations.?

Question

These are the equations that I need to solve.

1. b x 3^a = 400
3a - 2b =12

2.At Hungry macs, 3 hamburgers and 2 thickshakes cost $11.65. If 2 hamburgers and 5 thickshakes cost $ 12.90, what is the price of a hamburger?

Any help is much appreciated thanks.

Answer 1

#2 is pretty easy:

3h + 2t = 11.65
2h + 5t = 12.90

Use the second equation to solve for t:
t = (12.90 - 2h)/5

And substitute that into the first:

3h + 2t = 11.65
3h + 2(12.90 - 2h)/5 = 11.65
15h + 25.80 - 4h = 58.25
11h = 32.45
h = 2.95

The first is a lot harder.

Answer 2

No 2
Let H stand fot hamburger and T stand for thickshakes
so 3H+2T=11.65 (1)
2H+5T=12.90 (2)
Mult eq(1) by 2 6H+4T=23.30
Mult eq(2) by 3 6H+15T=38.70
Change signs in(1) -6H-4T =-23.30
Add (1) & (2) 11T=15.4
T=15.4/11 =1.40
& from (1) 3H+2*1.40=11.65
3H=11.65-2.80=8.85
&H=2.95
It might have been easier to multiply eq (1) by 5 and eq(2) by 2 and to have solved directly for H