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:
[tex]ax+by = c[/tex]
Here a, b and c are constants and x,y are variables.
In the given equations, after comparing with the general form
[tex]a_1 = 4\\b_1 = 5 \\c_1 = 10\\a_2 = A\\b_2 =B\\c_2 = 16[/tex]
"In order for a system of equations to have infinity many solutions,
[tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex] "
Putting the values we get
[tex]\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[/tex]
Hence,
For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.
