Question

Without Graphing, Is The System Independent, Dependent, Or Inconsistent? (Equation And Answer Choices Are In Comments!)

Answer 1

12x +3y = 12
y = -4x +5
 
We can convert the first equation to the same form as the second (y=mx+b, or slope-intercept).
 
12x +3y = 12
3y = -12x +12
y = -4x +4
 
Comparing the simplified first equation y = -4x +4 to the second equation y = -4x + 5, we see that both have the same slope (m = -4), but different y-intercepts (b = 4, b = 5). This means they are parallel lines, or an inconsistent system. There are no solutions.