Question

4x + 5y = 10

Answer 1

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:

$ax+by = c$

Here a, b and c are constants and x,y are variables.

In the given equations, after comparing with the general form

$a_1 = 4\\b_1 = 5 \\c_1 = 10\\a_2 = A\\b_2 =B\\c_2 = 16$

"In order for a system of equations to have infinity many solutions,

$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ "

Putting the values we get

$\frac{4}{A} = \frac{5}{B} = \frac{10}{16}\\\frac{4}{A} = \frac{5}{B} = \frac{5}{8}\\Now\\\frac{4}{A} = \frac{5}{8}\\\frac{A}{4} = \frac{8}{5}\\A = \frac{8}{5} * 4\\A = \frac{32}{5}\\And\\\frac{5}{B} = \frac{5}{8}\\\frac{B}{5} = \frac{8}{5}\\B = 8$

Hence,

For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.