system of equations

Question

Solve the following system of equations.

x+5y=5

 

x=4-5y

Answer 1

This is a bit of a tricky problem because it as no solution, as I will explain below:

x+5y=5

x=4-5y

The second equation can be rewritten as: x+5y=4

The issue is that one equation tells us that (x+5y) should equal 5, while the other equation says it should equal 4.

Therefore, a solution does not exist.

Message me if you have further questions.

Answer 2

Look at the slopes of the 2 given lines:

 

x + 5y = 5 ⇒y = -x/5 + 1 ⇒ m₁ = -1/5

 

x = 4 - 5y ⇒ y = -x/5 + 4/5 ⇒ m₂ = -1/5

 

The 2 lines have the same slope, but different y-intercepts.  Hence they are parallel, non intersecting lines, and there is no solution to this system.