y=1/2x+5 and 2y=x-24 Solve for x and y

Question

How do I solve for x and y?  I tried substituting y for 1/2x+5

So that means (1/2x+5)2=x-24

x=10=x-24 x=-34? y=-12 but it doesn't work when I substitute those answers into the equation.  Where is my mistake?

Answer 1

y = (1/2)x + 5 --- (1)
2y = x - 24 --- (2)

From (2), we have:

y = (1/2)x - 12 --- (3)

Compare (1) and (3).
Notice that we have y = (1/2)x + 5 and y = (1/2)x - 12 at the same time, something which is impossible.

Hence, there is no solution to the system of equations.

Comments

Thank you so much!  I really appreciate it.