# Solve for x1 and x2

#### frctl

##### Junior Member

I require help with this system the way it is presented
Where does the x1 and x2 go or with which coefficient?

#### Romsek

##### Full Member
You've never seen matrices before?

#### frctl

##### Junior Member
Yes I am learning them right now.

#### Romsek

##### Full Member
well just apply matrix subtraction and multiplication as you usually would.
First subtract $$\displaystyle \begin{pmatrix}3\\4\end{pmatrix}$$ from both sides then the first equation is

$$\displaystyle 1 \cdot x_1 + 2 \cdot x_2 = 6$$

I leave you to figure out the second equation

#### frctl

##### Junior Member
1 · x1 + 2 · x2 = 6
1 · x1 + 1 · x2 = 5

#### pka

##### Elite Member
View attachment 17443

I require help with this system the way it is presented
Where does the x1 and x2 go or with which coefficient?
View attachment 17443

I require help with this system the way it is presented
Where does the x1 and x2 go or with which coefficient?
$$\left[ {\begin{array}{*{20}{c}} 1&2 \\ 1&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 3 \\ 4 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 9 \\ 9 \end{array}} \right]$$ Subtract from both sides.
$$\left[ {\begin{array}{*{20}{c}} 1&2 \\ 1&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 6 \\ 5 \end{array}} \right]$$ Find the inverse.
$$\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 1&2 \\ 1&1 \end{array}} \right]^{-1} \left[ {\begin{array}{*{20}{c}} 6 \\ 5 \end{array}} \right]$$

#### frctl

##### Junior Member
I found the inverse is

-1 2
1 -1

How does this help me solve for x1 and x2

#### frctl

##### Junior Member
Ah wait if I multiply them out I obtain

x1 = 4
x2 = 1

#### Subhotosh Khan

##### Super Moderator
Staff member
Ah wait if I multiply them out I obtain

x1 = 4
x2 = 1

#### frctl

##### Junior Member
How do I check my answer in this case

#### pka

##### Elite Member
How do I check my answer in this case
Go on, frctl, don't be obtuse. Substitute the values into the equation in the OP. See if they work.

Yes I obtain
6
5

Thank you

#### Subhotosh Khan

##### Super Moderator
Staff member
Yes I obtain
6
5

Thank you
What do you mean by:

6
5

what are those?

the matrix
x1 and x2

#### Otis

##### Senior Member
the matrix
x1 and x2
That's not correct, frctl. You already posted your solution: x1=4 and x2=1 (post #8).

The second equation in post #6 shows the matrix containing elements 6 and 5.

We need to be more careful with language.