# What is the best method to solve the system : substitution or elimination x-y=6 -2x+2y=1

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Given equations are :

x-y = 6.....................(1)

-2x+2y = 1..............(2).

If we simplify the second equation by dividing by -2, we get:

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

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

We see that the equations (1) and (3) are representing a pair of straight lines which never meet with a distance of {1-(-1/2)}/sqrt{(1^1+(-1)^2} = 1.5/sqrt2 = 3sqrt/4 between the lines.

Therefore is no common solution for the given straight lines. So **both substitution and elimination methods fail** to give a solution.

We can use either method, but **substitution is probably slightly easier**.

We’ll solve the first equation for x and we'll substitute it into the second equation.

x = 6 + y

-2(6 + y)+2y=1

We'll remove the brackets:

-12 - 2y + 2y = 1

We'll eliminate like terms and we'll get:

-12 = 1

Since there is not a mistake in our calculus, the lines described by the equations above, are parallel.

y = x - 6

m1 = 1

2y = 2x + 1

We'll divide by 2:

y = x + 1/2

m2 =1

Since the slopes of the lines are equal, the lines are parallel.

**The system has no solution, since the lines have no intercepting point.**