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Sagot :
The system of equations:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]This comes from the fact that if we multiply the first equation by 3 then we have:
[tex]3x-18y=12[/tex]But this clearly contradicts the second one. Then the system has no solutions.
a.
To find a system with one solution we only have to change one of the coefficients of the equation. If we change the first x coefficient from 1 to 2. then we have the system:
[tex]\begin{gathered} 2x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]which has one solution.
b.
To find a system with an infinite number of solutions we can change the constant of the second equation to 12, then:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=12 \end{gathered}[/tex]then if we multiply the first by 3 then we have the second one, therefore the equations are the same and the system will have and infinite number os solutions.
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