To determine how many solutions this linear system has, we need to analyze the two equations provided.
The first equation is:
y = 2x + 5
This represents a straight line with a slope of 2 and a y-intercept of 5.
The second equation is:
8x – 4y = 20
To understand this equation better, we can rearrange it to the slope-intercept form (y = mx + b).
First, we can rewrite the equation:
-4y = -8x + 20
Dividing everything by -4 gives us:
y = 2x – 5
This shows that the second line also has a slope of 2 but a different y-intercept (-5).
Now we can see that both lines have the same slope (2) but different y-intercepts (5 and -5). Since parallel lines never intersect, this system of equations has no solutions.
In conclusion, the linear system given has no solutions because the two equations represent parallel lines that never meet.