Answer:
Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x
Thus, option A) is true.
The solution to the system of equations be:
![x = 4, y = 5](https://tex.z-dn.net/?f=x%20%3D%204%2C%20y%20%3D%205)
Step-by-step explanation:
It is important to remember that when we solve the system of equations, the first step we need to do is to solve one of the equations for one of the variables.
Given the system of equations
![x - y = -1](https://tex.z-dn.net/?f=x%20-%20y%20%3D%20-1)
![2x - y = 3](https://tex.z-dn.net/?f=2x%20-%20y%20%3D%203)
Step 1: Solve one of the equations for one of the variables. Let's solve the first equation for x
![x-y=-1](https://tex.z-dn.net/?f=x-y%3D-1)
Add y to both sides
![x-y+y=-1+y](https://tex.z-dn.net/?f=x-y%2By%3D-1%2By)
![x=-1+y](https://tex.z-dn.net/?f=x%3D-1%2By)
Thus, option A) is true.
<u>NOW LET US SOLVE THE REMAINING PORTION</u>
to solve for y
![\begin{bmatrix}2\left(-1+y\right)-y=3\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2%5Cleft%28-1%2By%5Cright%29-y%3D3%5Cend%7Bbmatrix%7D)
![-2+y=3](https://tex.z-dn.net/?f=-2%2By%3D3)
![y=5](https://tex.z-dn.net/?f=y%3D5)
For x = -1 + y
substitute y = 5
![x=-1+5](https://tex.z-dn.net/?f=x%3D-1%2B5)
![x=4](https://tex.z-dn.net/?f=x%3D4)
Thus, the solution to the system of equations be:
![x = 4, y = 5](https://tex.z-dn.net/?f=x%20%3D%204%2C%20y%20%3D%205)
Answer:
Z = 0.198877274
Step-by-step explanation:
![(\frac{1}{4})^{3z-1} = 16^z + 2*16^{z-2}\\4^{1-3z} = 4^{2z} + 4^{\frac{1}{2}}*4^{2z-4}\\4^{1-3z} = 4^{2z} + 4^{2z-4+\frac{1}{2}}\\4^{1-3z} = 4^{2z} + 4^{2z-\frac{7}{2}}\\4^{1-3z} = 4^{2z} *(1+ 4^{-\frac{7}{2}})\\4^{1-3z} = 4^{2z} *(1+ 2^{-7})\\4^{1-3z} = 4^{2z} *(1+ \frac{1}{128} )\\4^{1-3z} = 4^{2z} *(\frac{129}{128} )\\Taking\;\; Logarithm\;\; with\;\; base\;\; 4\\Log_4(4^{1-3z}) = Log_4(4^{2z}) + Log_4(\frac{129}{128})\\1-3z = 2z + 0.005613627712 \\5z = 0.994386372\\z = 0.198877274](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B3z-1%7D%20%3D%2016%5Ez%20%2B%202%2A16%5E%7Bz-2%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2B%204%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%2A4%5E%7B2z-4%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2B%204%5E%7B2z-4%2B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2B%204%5E%7B2z-%5Cfrac%7B7%7D%7B2%7D%7D%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%281%2B%204%5E%7B-%5Cfrac%7B7%7D%7B2%7D%7D%29%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%281%2B%202%5E%7B-7%7D%29%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%281%2B%20%5Cfrac%7B1%7D%7B128%7D%20%29%5C%5C4%5E%7B1-3z%7D%20%3D%204%5E%7B2z%7D%20%2A%28%5Cfrac%7B129%7D%7B128%7D%20%29%5C%5CTaking%5C%3B%5C%3B%20Logarithm%5C%3B%5C%3B%20with%5C%3B%5C%3B%20base%5C%3B%5C%3B%204%5C%5CLog_4%284%5E%7B1-3z%7D%29%20%3D%20Log_4%284%5E%7B2z%7D%29%20%2B%20Log_4%28%5Cfrac%7B129%7D%7B128%7D%29%5C%5C1-3z%20%3D%202z%20%2B%200.005613627712%20%5C%5C5z%20%3D%200.994386372%5C%5Cz%20%3D%200.198877274)
Hence, the value of Z = 0.198877274