Answer:
x=2
y = 0
Step-by-step explanation:
3x + y = 6 -------------(i)
5x - 2y = 10 -------------(ii)
Multiply (i) by 2 ===> 6x +2y = 12
(ii) ===> <u> 5x - 2y = 10</u>
add ============> 11x = 22
x = 22/11
x = 2
Substitute x = 2 in (i)
3*2 + y = 6
6 + y = 6
y = 6 - 6
y = 0
Answer:
![\:c_{11}=-2,\:\:\:c_{12}=-2](https://tex.z-dn.net/?f=%5C%3Ac_%7B11%7D%3D-2%2C%5C%3A%5C%3A%5C%3Ac_%7B12%7D%3D-2)
![\:c_{21}=5,\:\:\:c_{22}=8](https://tex.z-dn.net/?f=%5C%3Ac_%7B21%7D%3D5%2C%5C%3A%5C%3A%5C%3Ac_%7B22%7D%3D8)
Step-by-step explanation:
Given the matrices
![A=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}](https://tex.z-dn.net/?f=A%3D%5Cbegin%7Bpmatrix%7D1%26-1%5C%5C%202%261%5Cend%7Bpmatrix%7D)
![B=\begin{pmatrix}1&2\\ \:3&4\end{pmatrix}](https://tex.z-dn.net/?f=B%3D%5Cbegin%7Bpmatrix%7D1%262%5C%5C%20%5C%3A3%264%5Cend%7Bpmatrix%7D)
Calculating AB:
![\begin{pmatrix}1&-1\\ \:\:2&1\end{pmatrix}\times \:\begin{pmatrix}1&2\\ \:\:3&4\end{pmatrix}=\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7D1%26-1%5C%5C%20%5C%3A%5C%3A2%261%5Cend%7Bpmatrix%7D%5Ctimes%20%5C%3A%5Cbegin%7Bpmatrix%7D1%262%5C%5C%20%5C%3A%5C%3A3%264%5Cend%7Bpmatrix%7D%3D%5Cbegin%7Bpmatrix%7Dc_%7B11%7D%26c_%7B12%7D%5C%5C%20%5C%3A%5C%3A%5C%3Ac_%7B21%7D%26c_%7B22%7D%5Cend%7Bpmatrix%7D)
Multiply the rows of the first matrix by the columns of the second matrix
![=\begin{pmatrix}1\cdot \:1+\left(-1\right)\cdot \:3&1\cdot \:2+\left(-1\right)\cdot \:4\\ 2\cdot \:1+1\cdot \:3&2\cdot \:2+1\cdot \:4\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D1%5Ccdot%20%5C%3A1%2B%5Cleft%28-1%5Cright%29%5Ccdot%20%5C%3A3%261%5Ccdot%20%5C%3A2%2B%5Cleft%28-1%5Cright%29%5Ccdot%20%5C%3A4%5C%5C%202%5Ccdot%20%5C%3A1%2B1%5Ccdot%20%5C%3A3%262%5Ccdot%20%5C%3A2%2B1%5Ccdot%20%5C%3A4%5Cend%7Bpmatrix%7D)
![=\begin{pmatrix}-2&-2\\ 5&8\end{pmatrix}](https://tex.z-dn.net/?f=%3D%5Cbegin%7Bpmatrix%7D-2%26-2%5C%5C%205%268%5Cend%7Bpmatrix%7D)
Hence,
![\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}=\begin{pmatrix}-2&-2\\ \:5&8\end{pmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bpmatrix%7Dc_%7B11%7D%26c_%7B12%7D%5C%5C%20%5C%3A%5C%3A%5C%3Ac_%7B21%7D%26c_%7B22%7D%5Cend%7Bpmatrix%7D%3D%5Cbegin%7Bpmatrix%7D-2%26-2%5C%5C%20%5C%3A5%268%5Cend%7Bpmatrix%7D)
Therefore,
![\:c_{11}=-2,\:\:\:c_{12}=-2](https://tex.z-dn.net/?f=%5C%3Ac_%7B11%7D%3D-2%2C%5C%3A%5C%3A%5C%3Ac_%7B12%7D%3D-2)
![\:c_{21}=5,\:\:\:c_{22}=8](https://tex.z-dn.net/?f=%5C%3Ac_%7B21%7D%3D5%2C%5C%3A%5C%3A%5C%3Ac_%7B22%7D%3D8)
Answer:
<em>I earned $856 on the first day</em>
Step-by-step explanation:
Let's call
x = earning on the second day
2x = earnings on the first day
3x = earnings on the third day
The total earnings are $2568, thus
x + 2x + 3x = 2568
Simplifying:
6x = 2568
Dividing by 6:
x = 2568/6
x = 428
I earned $428 on the second day.
2x = 2*$428 = $856
I earned $856 on the first day
1 + 5 = 6
3 + 3 = 6
3 + 47 = 50
7 + 43 = 50
13 + 37 = 50
19 + 31 = 50