Question

2]How many solutions does the system of equations have?y = 4x - 9y = 2x + 5 No SolutionInfinite SolutionsOne Solution

Answer 1

Let's solve the system to see how many solutions have.

The system is:

`\begin{cases}y=4x-9 \\ y=2x+5\end{cases}`

Then we can euqal the two equations:

`4x-9=2x+5`

And solve for x:

`\begin{gathered} 4x-2x=5+9 \\ 2x=14 \\ x=(14)/(2) \\ x=7 \end{gathered}`

Since we have a defined value for x, the system has only one solution.

To have no solutions is to get an aswer like:

`1=0`

Which can never be true.

To have infinte solutions, is to get an asnwer of the form:

`0=0`

But, in this case, we have a exact value for x, then the system has 1 solution.