To check if the solution is correct, we will substitute x=3 and x=1 in both equations and make sure the left-hand side and right-hand side are equal in both of them.
x+5y=8 & (I) - x+2y=-1 & (II)
(I), (II): x= 3, y= 1
3+5( 1)? =8 - 3+2( 1)? =-1
(I), (II): a * 1=a
3+5 ? = 8 -3+2 ? = -1
(I), (II): Add terms
8=8 -1=-1
The solution is correct.
c Since the second equation is in slope-intercept form, let's rewrite the first equation on this form as well.
Having rewritten the equations, we see that they have the same slope but different y-intercepts. This makes them parallel lines, which means they do not intersect. Thus, this system of equations does not have any solution.
