MHB Solve Financial Equation: (2,3) & (3,1) = (1,4)

[nickoh]

Hi,

I'm hoping someone can please help me with this. I'm sure it's quite simple, but I can't get my head around it.

Essentially I need to get:

(2,3) and (3,1) to equal (1,4).

The numbers in each bracket form pay off scenarios for different securities. I need to find out how to get what amount of (2,3) and (3,1) (can be added or subtracted) will equal (1,4).

i.e. assume (2,3) is x and (3,1) is y
2x + 0.5y = (1,4)

Obviously this is incorrect, but it helps to give a picture of what I need to work out.

I'm actually stumped (I've never been good at this). Every time I try using guess and check I can get one side to work out, but not the other.

Hopefully somebody can please help me understand!

 

[nickoh]

Tell me, is this correct? Or am I way off?

2x + 3y = 1
3x + 1y = 4

Therefore:

3(3x + 1y = 4)
9x + 3y = 12

9x + 3y =12
-
2x + 3y = 1

7x + 0y = 11

x = 1.5714
y = -0.714

 

[M R]

Tell me, is this correct? Or am I way off?

2x + 3y = 1
3x + 1y = 4

Therefore:

3(3x + 1y = 4)
9x + 3y = 12

9x + 3y =12
-
2x + 3y = 1

7x + 0y = 11

x = 1.5714
y = -0.714

Those are the numbers I got too. I prefer 11/7 and -5/7 though.

 

[nickoh]

Thanks M R,

I'm hoping we are both correct, it seems logical. I've clearly forgotten a lot of maths since my high school days!