No solutions- equations never intersect (parallel lines)
Explanation:
First, let's convert our second equation into slope-intercept form
y
=
m
x
+
b
Let's subtract
2
x
from both sides to get
−
y
=
−
2
x
+
2
Next, divide all terms by
−
1
to get
y
=
2
x
−
2
We see that our slope, the coefficient on the
x
term, is
2
. This equation has the same slope as the first.
It is important to realize that when two lines have the same slope, it means they are parallel. This means they never intersect.
Since they never intersect, it means this system has no solution.
Hope this helps!
2d = 5c
2/5 = c/d ...true
5/2 = d/c...true
2/c = 5/d...true
2/d = 5/c....not true
