Question

Solve the system using the substitution or elimination method. How many solutions are there to this system?

Answer 1

Answer:

$-3*(3y+2) + 9y = -6$

$-9y -6 + 9y = -6$

$-6=-6$

So then as we can see we can have infinite solutions.

$S= [(x, \frac{x-2}{3}) , x \in R]$

Step-by-step explanation:

Assuming the following system of equations:

$2x-6y =4$   (1)

$-3x+9y =-6$   (2)

For this case we can use the substitution method in order to find the possible solutions for the system.

If we solve for x from equation (1) we got:

$2x = 6y +4$

$x = 3y +2$   (3)

Now we can replace equation (3) into equation (2) and we got:

$-3*(3y+2) + 9y = -6$

$-9y -6 + 9y = -6$

$-6=-6$

So then as we can see we can have infinite solutions.

And the possible solutions are for a fixed value of x, we can solve y from equation (3) and we got:

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

So the solution would be: $S= [(x, \frac{x-2}{3}) , x \in R]$