HOW MANY SOLUTIONS DOES THE LINEAR SYSTEM HAVE?

Y=2X+4
Y=2

2=2x+4

-2=2x
-1=x

One solution?... if I read the question correctly.

To determine how many solutions the linear system has, we need to compare the two equations and analyze their relationship.

The given system of equations is:

Y = 2X + 4
Y = 2

Notice that the second equation is a horizontal line, Y = 2, which means that for every value of X, the value of Y will always be 2. This second equation has a consistent value for Y and doesn't depend on the value of X.

Looking at the first equation, Y = 2X + 4, we can see that it represents a line with a slope of 2 and a y-intercept of 4. This equation represents a line that increases as X increases and has a different Y value for different X values.

Since the second equation, Y = 2, represents a horizontal line, it will intersect the first equation, Y = 2X + 4, at a single point. So, the linear system has a unique solution (one solution).

To visually confirm the solution, we could plot the two equations on a graph and observe where they intersect.