Answer:
no solution ever
Step-by-step explanation:
https://simplisico.com/share/q/B8ZG0KyiS5OVu7vDDhWMr37x
System of equations [tex]y - 6x = -3 , \ \ \ 4y -24x = -16[/tex] has no solution.
" System of equations is defined as the finite number of equations with common solution."
Different condition for solution of system of equations:
[tex]a_{1} x+ b_{1}y + c_{1} =0\\ \\a_{2} x+ b_{2}y + c_{2} =0[/tex]
Exactly one solution : [tex]\frac{a_{1} }{ a_{2}}\neq \frac{b_{1} }{ b_{2}}[/tex]
Infinitely many solution : [tex]\frac{a_{1} }{ a_{2}}=\frac{b_{1} }{ b_{2}}=\frac{c_{1} }{c_{2}}[/tex]
No solution : [tex]\frac{a_{1} }{ a_{2}}=\frac{b_{1} }{ b_{2}}\neq \frac{c_{1} }{c_{2}}[/tex]
According to the question,
Given system of equations,
[tex]y - 6x = -3 , \\ \\4y -24x = -16[/tex]
Substitute the value in the condition for solution of system of equations we get,
[tex]\frac{1}{4} = \frac{-6}{-24}\neq \frac{-3}{-16}\\ \\\implies \frac{1}{4} = \frac{1}{4} \neq \frac{-3}{-16}[/tex]
Hence, given system of equations has no solutions.
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