Answer:
For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.
Step-by-step explanation:
Given equations are:
4x + 5y = 10
Ax + By = 16
The general form of linear equation in two variables is given by:
![ax+by = c](https://tex.z-dn.net/?f=ax%2Bby%20%3D%20c)
Here a, b and c are constants and x,y are variables.
In the given equations, after comparing with the general form
![a_1 = 4\\b_1 = 5 \\c_1 = 10\\a_2 = A\\b_2 =B\\c_2 = 16](https://tex.z-dn.net/?f=a_1%20%3D%204%5C%5Cb_1%20%3D%205%20%5C%5Cc_1%20%3D%2010%5C%5Ca_2%20%3D%20A%5C%5Cb_2%20%3DB%5C%5Cc_2%20%3D%2016)
"In order for a system of equations to have infinity many solutions,
"
Putting the values we get
![\frac{4}{A} = \frac{5}{B} = \frac{10}{16}\\\frac{4}{A} = \frac{5}{B} = \frac{5}{8}\\Now\\\frac{4}{A} = \frac{5}{8}\\\frac{A}{4} = \frac{8}{5}\\A = \frac{8}{5} * 4\\A = \frac{32}{5}\\And\\\frac{5}{B} = \frac{5}{8}\\\frac{B}{5} = \frac{8}{5}\\B = 8](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7BA%7D%20%3D%20%5Cfrac%7B5%7D%7BB%7D%20%3D%20%5Cfrac%7B10%7D%7B16%7D%5C%5C%5Cfrac%7B4%7D%7BA%7D%20%3D%20%5Cfrac%7B5%7D%7BB%7D%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5C%5CNow%5C%5C%5Cfrac%7B4%7D%7BA%7D%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5C%5C%5Cfrac%7BA%7D%7B4%7D%20%3D%20%5Cfrac%7B8%7D%7B5%7D%5C%5CA%20%3D%20%5Cfrac%7B8%7D%7B5%7D%20%2A%204%5C%5CA%20%3D%20%5Cfrac%7B32%7D%7B5%7D%5C%5CAnd%5C%5C%5Cfrac%7B5%7D%7BB%7D%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5C%5C%5Cfrac%7BB%7D%7B5%7D%20%3D%20%5Cfrac%7B8%7D%7B5%7D%5C%5CB%20%3D%208)
Hence,
For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.
Answer:
B
Step-by-step explanation:
Triangle B because 128°>90°
Answer:
Solve in terms of the arbitrary variable x . x = 5 5 = − 2
Step-by-step explanation: