There are many ways to do this, even without investigating first.

But I see that there are 3 equations given while there are only two unknowns or variables. We need only two independent equations to solve for two unknowns. The 3rd extraneous equation could mean trouble.

300x + 100y = 900 ----------(1)

400x + 200y = 2200 --------(2)

100x + 200y = 800 -----------(3)

Since they are all in 100's, let us reduce them all into their simplest forms by dividing them all by 100,

3x + y = 9 -----------------(1a)

4x + 2y = 22 --------------(2a)

x + 2y = 8 ----------------(3a)

Since there are only two unknowns, we will use only to equations and then let us see if the 3rd equation will accept the solved x and y from the said two equations.

Let's use (1a) and (2a) only.

One popular way of doing this is by substitution.

From (1a), y = 9 -3x

Substitute that into (2a),

4x +2(9 -3x) = 22

4x +18 -6x = 22

4x -6x = 22 -18

-2x = 4

x = 4 / -2

x = -2 ------------------------------**

And, y = 9 -3(-2) = 9 +6 = 15 -------**

Would the Eq.(3a) be satisfied with those?

x + 2y = 8 ----------------(3a)

-2 +2(15) =? 8

-2 +30 =? 8

28 =? 8

No!

Trouble, just as I thought.

What it means is that the 3 given independent equations do not have a common point they can agree on. :-)

Meaning, for the 3 given equations, there is no solution.