Answer: First option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept
We need to write each equation in Slope-Intercept form:
First equation
[tex]3y + 12 = 6x\\\\3y=6x-12\\\\y=2x-4[/tex]
Second equation
[tex]2y = 4x + b \\\\y=2x+\frac{b}{2}[/tex]
Since, by definition, a system of linear equations has infinitely many solutions when the lines are the same, we can say that:
[tex]y=y\\\\2x-4=2x+\frac{b}{2}[/tex]
Then, solving for "b", we get:
[tex]-4=\frac{b}{2}\\\\(-4)(2)=b\\\\b=-8[/tex]
