Since the slopes of the two lines are the not equal, they will have only one solution. The solution will be a point and can be found using the method given below.
We can find the solutions by simultaneously solving the two equations.
From first equation, the value of y comes out to be:
[tex]2x+3y=-3 \\ \\
3y=-3-2x \\ \\
y= \frac{-3-2x}{3} [/tex]
Using this value of y in second equation, we get:
[tex]3x+5( \frac{-3-2x}{3} )=-9 \\ \\
9x-15-10x=-27 \\ \\
-x=-27+15 \\ \\
-x=-12 \\ \\
x=12[/tex]
Using this value of x, we can find y:
[tex]y= \frac{-3-2x}{3}= \frac{-3-24}{3} =-9 [/tex]
Therefore, there is only one solution to the given equations is which is (12, -9)
