Answer:
[tex] -3*(3y+2) + 9y = -6[/tex]
[tex] -9y -6 + 9y = -6[/tex]
[tex]-6=-6[/tex]
So then as we can see we can have infinite solutions.
[tex]S= [(x, \frac{x-2}{3}) , x \in R][/tex]
Step-by-step explanation:
Assuming the following system of equations:
[tex] 2x-6y =4[/tex] (1)
[tex] -3x+9y =-6[/tex] (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:
[tex] 2x = 6y +4[/tex]
[tex] x = 3y +2 [/tex] (3)
Now we can replace equation (3) into equation (2) and we got:
[tex] -3*(3y+2) + 9y = -6[/tex]
[tex] -9y -6 + 9y = -6[/tex]
[tex]-6=-6[/tex]
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:
[tex] y = \frac{x-2}{3}[/tex]
So the solution would be: [tex]S= [(x, \frac{x-2}{3}) , x \in R][/tex]
