# Find X and Y

• Oct 20th 2008, 08:21 PM
sarah3asal
Find X and Y
Hello.. Could someone pleaseee help me find X and Y and show me the steps how you got it?

300x + 100y = 900
400x + 200y = 2200
100x + 200y = 800
• Oct 20th 2008, 10:23 PM
ticbol
Quote:

Originally Posted by sarah3asal
Hello.. Could someone pleaseee help me find X and Y and show me the steps how you got it?

300x + 100y = 900
400x + 200y = 2200
100x + 200y = 800

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.