Question

Solve the system of equations by graphing , then classify the system as consistent or inconsistent and as dependent or independent

5x-9y=45
9y-5x=-45

and what is the solution? or is their no solution

Answer 1

Rewrite each equation in terms of y and then graph them.

Answer 2

The solution if it exists is the intersection of the two lines.

Answer 3

If there is only one line then there are an infinite number of solutions, if the lines are parallel there are no solutions.

Answer 4

for eq. 5x-9y=45
-9y=45-5x
for eq.9y-5x=-45
9y=-45+5x

note: The slopes area the same as well as the y-intercepts. HEnce, the system is consistent and the equations are dependent.
therefore its consistent and dependent

Answer 5

5x-9y=45 Let x =0, then y= -5 coordinate = (0, -5)
Let y =0, then x= 9 coordinate = (9, 0)

Plot these points and draw a line through them


9y-5x=-45 Let x =0, then y= -5 coordinate = (0, -5)
Let y =0, then x= 9 coordinate = (9, 0)

They are the same equation and hence cannot be solved simultaneously for one value of x and y.

Answer 6

Solution set S:
\[S=\left\{\left(\begin{matrix}9 \\ 0\end{matrix}\right) + t \left(\begin{matrix}9/5 \\ 1\end{matrix}\right)\| t \in \mathbb{R}\right\}\]