Question

Determine which system below will produce infinitely many solutions.

Answer 1

The solution is 

2x + 5y = 24
2x + 5y = 42

2x + 5y = 24, and then 2x + 5y = 24, and so on...

Answer 2

Answer:

4x - 3y = 9

-8x + 6y = -18

Step-by-step explanation:

Since, a system of equation,

$a_1x+b_1y = c_1$ , $a_2x+b_2y=c_2$

Then the system has infinitely many solution if,

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

For the system of equations,

2x + 5y = 24

2x + 5y = 42

$\frac{2}{2}=\frac{5}{5}\neq \frac{24}{42}$

⇒ This system does not have infinitely many solutions,

Now, For the system of equations,

3x - 2y = 15

6x + 5y = 11

$\frac{3}{6}\neq \frac{-2}{5}\neq \frac{15}{11}$

⇒ This system does not have infinitely many solutions,

For the system of equations,

4x - 3y = 9

-8x + 6y = -18

$\frac{4}{-8}=\frac{-3}{6}= \frac{9}{-18}=-2$

⇒ This system has infinitely many solutions,

For the system of equations,

5x - 3y = 16

-2x + 3y = -7

$\frac{5}{-2}\neq \frac{-3}{3}\neq \frac{16}{-7}$

⇒ This system does not have infinitely many solutions,