Question

given the equation y=2/3x+4 find each of the following:an equation so that the system would have infinite solutions.an equation so that the system would have one solution.an equation so that the system would have no solutions.

Answer 1

we are given the following equation:

`y=(2)/(3)x+4`

An equation so that the system has an infinite solution is an equation that is equivalent to this equation, for example:

`\begin{gathered} y=(2)/(3)x+4,(1) \\ 3y=2x+12,(2) \end{gathered}`

In this case, equation (2) is equal to equation one multiplied by three.

For the system to have a solution the equations must have a different slope, for example:

`\begin{gathered} y=(2)/(3)x+4,(1) \\ y=4x+4,(2) \end{gathered}`

For the system to have no solutions, their slopes must be equal but not their y-intercept, for example:

`\begin{gathered} y=(2)/(3)x+4,(1) \\ y=(2)/(3)x+5,(2) \end{gathered}`