Question

How many solutions 2x+3y=-3 and 3x + 5y = -9

Answer 1

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:

$2x+3y=-3 \\ \\ 3y=-3-2x \\ \\ y= \frac{-3-2x}{3}$

Using this value of y in second equation, we get:

$3x+5( \frac{-3-2x}{3} )=-9 \\ \\ 9x-15-10x=-27 \\ \\ -x=-27+15 \\ \\ -x=-12 \\ \\ x=12$

Using this value of x, we can find y:

$y= \frac{-3-2x}{3}= \frac{-3-24}{3} =-9$

Therefore, there is only one solution to the given equations is which is (12, -9)