Answer:
4x - 3y = 9
-8x + 6y = -18
Step-by-step explanation:
Since, a system of equation,
[tex]a_1x+b_1y = c_1[/tex] , [tex]a_2x+b_2y=c_2[/tex]
Then the system has infinitely many solution if,
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
For the system of equations,
2x + 5y = 24
2x + 5y = 42
[tex]\frac{2}{2}=\frac{5}{5}\neq \frac{24}{42}[/tex]
⇒ This system does not have infinitely many solutions,
Now, For the system of equations,
3x - 2y = 15
6x + 5y = 11
[tex]\frac{3}{6}\neq \frac{-2}{5}\neq \frac{15}{11}[/tex]
⇒ This system does not have infinitely many solutions,
For the system of equations,
4x - 3y = 9
-8x + 6y = -18
[tex]\frac{4}{-8}=\frac{-3}{6}= \frac{9}{-18}=-2[/tex]
⇒ This system has infinitely many solutions,
For the system of equations,
5x - 3y = 16
-2x + 3y = -7
[tex]\frac{5}{-2}\neq \frac{-3}{3}\neq \frac{16}{-7}[/tex]
⇒ This system does not have infinitely many solutions,
