Answer:
x = 1
Step-by-step explanation:
Given the matrix;
![-2\left[\begin{array}{ccc}x&-1\\3&5\end{array}\right] + \left[\begin{array}{ccc}3&8\\-1&6\end{array}\right] = \left[\begin{array}{ccc}x&10\\-7&-4\end{array}\right]](https://tex.z-dn.net/?f=-2%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%26-1%5C%5C3%265%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%268%5C%5C-1%266%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%2610%5C%5C-7%26-4%5Cend%7Barray%7D%5Cright%5D)
Converting to equations
From the first row of each matrices
-2x + 3 = x
Collect the like terms
-2x - x = -3
-3x = -3
x = -3/-3
x = 1
Hence the value of x is 1
z is directly proportional to x: z = kx.
If z is directly proportional to x and inversely proportional to y, then z = Kx/y.
When x= 6 and y = 6, z is 12. Find the constant of proportionality, K:
12 = K(6/6), or K = 12
Then, in general, z = 12x/y.
What is z when x=13 and y=10? z = 12(13)/(10) = 15.6 (answer)