EXPLANATION
Given the system of equations:
(1) 2x + 6y = -3
(2) 2x + 6y = 0
Subtract 6y from both sides:
2x + 6y - 6y = -3 - 6y
Simplify:
2x = -3 - 6y
Divide both sides by 2:
[tex]\frac{2x}{2}=-\frac{3}{2}-\frac{6y}{2}[/tex]Simplify:
[tex]x=\frac{-3-6y}{2}[/tex]Substitute:
[tex]x=\frac{-3-6y}{2}[/tex][tex]2\cdot\frac{-3-6y}{2}+6y\text{ = 0}[/tex]Simplifying:
[tex]-3-6y+6y=0[/tex]Adding like terms:
[tex]-3=0[/tex]-3=0 is false, therefore the system of equations has no solutions.
The answer is the option C.
