Question

Solve the system. Is the answer (3,0) or (0, -1) or no solution or infinitely many solutions?

Answer 1

Given:

`\begin{gathered} (1)/(3)x+y=1\ldots..(1) \\ 2x+6y=6\ldots\text{.}(2) \end{gathered}`

Solve the system of equations.

Equation (2) can be simplified as,

`\begin{gathered} 2x+6y=6 \\ \text{Divide by 6 on both sides} \\ (2x)/(6)+(6y)/(6)=(6)/(6) \\ (1)/(3)x+y=1\text{ which represents the equation (1)} \end{gathered}`

Moreover, the slope and y-intercept of both the equation of lines are the same.

It shows that the lines are coincident.

The system has an infinite number of solutions. Also, point (3,0) is one of the solutions.