Answer:
y = x + 4
Step-by-step explanation:
The system will have one solution if the second equation has a slope that is different from the slope in the first equation.
The first equation is ...
y = 2x +4
It is of the form ...
y = mx + b
where m is the slope, and b is the y-intercept.
Any equation with the same slope (x-coefficient) will have a graph that is coincident with, or parallel to y = 2x+4. So, for the system to have exactly one solution, the slope must be different.
The offered equations all have an x-coefficient of 2, except the last one:
y = x +4 . . . . . x-coefficient is not 2.
This is the equation that will give one solution when graphed with the given equation.
