# A-Team Confluence Page

Starting with system of equations:

x+2y+10a+0b = 30

2x+4y+6a+0b = 20

2x+8y+0a+6b=40

We need to find the values for and b. Problem is we have three equations and four unknowns.

Write an augmented matrix using the above equations.

\left|\begin{array}{cccc | c} 1 & 2 & 10 & 0 & 30 // 2 & 4 & 6 & 0 & 20 // 2 & 8 & 0 & 6 & 40 \end{array}\right|

Begin row-reduction techniques.

\left|\begin{array}{cccc | c} 0 & 0 & 7 & 0 & 20 // 1 & 2 & 3 & 0 & 10 // 2 & 8 & 0 & 6 & 40 \end{array}\right|

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1. What is the task exactly?

2. I think I'll just plug the augmented matrix into Wolfram

3. Simplifies to

{{1,0,0,-3,-120/7}, {0,1,0,3/2,65/7},{0,0,1,0,20/7}}

4. So a = 20/7

5. x-3b = -120/7

2y+3b = 120/7

so

x+2y=10/7

x+y-1.5b=-55/7

then

10/7 + y - 1.5b +-55/7

y-(3/2)b=-65/7

FINALLY

b=(130/21)-(2/3)y

6. Wait! Using the solution for A, rewrite the equations by moving A to the side of constants. I get

x+2y+0b = (30-10a)

2x+4y+0b = (20-6a)

2x+8y+6b = 40

Wait, never mind. the first  two equations are linearly dependent on each other

7. Here is my solution page:

A-Team, solution method 2

8. With the new blue equations, I solved for the b variable! Using wolframalpha row reduction

B=130

A still equals 20/7

New equations:

10x+6y+2a=10

x+12y+4b=10

4x+4y+10b=30

9. Here are the other images!