Answer:
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Solution of the given system of equations
x = 3 and y= 2
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given system of equations are
4x - y = 10 ...(i)
8x +5y = 34...(ii)
The matrix form
A X = B
![\left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}10\\34\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-1%5C%5C8%265%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%5C%5C34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Step(ii):-</em></u>
<u><em>By using matrix inversion method</em></u>
<u><em></em></u>
<u><em></em></u>
<u><em></em></u>
|A| = ad-b c = 4(5) - 8(-1) = 20+8 = 28
Given matrix
![A = \left[\begin{array}{ccc}4&-1\\8&5\\\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%26-1%5C%5C8%265%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![AdjA = \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=AdjA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![A djA = \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]](https://tex.z-dn.net/?f=A%20djA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Inverse of the matrix
<u><em></em></u>
![A^{-1} = \frac{1}{|A|} A djA =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B%7CA%7C%7D%20A%20djA%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Step(iii)</em></u>:-
The solution of the given system of equations by using matrix inversion method
X = A⁻¹ B
![X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5&1\\-8&4\\\end{array}\right]\left[\begin{array}{ccc}10\\34\\\end{array}\right]](https://tex.z-dn.net/?f=X%20%3D%20A%5E%7B-1%7DB%20%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%261%5C%5C-8%264%5C%5C%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D10%5C%5C34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![X = A^{-1}B =\frac{1}{28} \left[\begin{array}{ccc}5X10+1X34\\-8X10+4X34\\\end{array}\right]](https://tex.z-dn.net/?f=X%20%3D%20A%5E%7B-1%7DB%20%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5X10%2B1X34%5C%5C-8X10%2B4X34%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] =\frac{1}{28} \left[\begin{array}{ccc}84\\56\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cfrac%7B1%7D%7B28%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D84%5C%5C56%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u><em>Final answer</em></u>:-
Solution of the given system x = 3 and y= 2
Answer:
In exact form it is w=-33/8
In decimal form it is w=-4.125
In mixed number form it is w=-4 1/8
Step-by-step explanation:
Answer:
x=
or 2.8
Step-by-step explanation:
combine like terms 2x-7x = -5x
subtract 12 from both sides to get -2-12 which = -14
-5x = -14
x=![\frac{14}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B5%7D)
Answer:
19250
Step-by-step explanation:
2750*7=19250