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.