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

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The equations to be solved are

x - y = 6 ...(1)

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

Using substitution x - y = 6 => x = 6 + y

substitute in -2x + 2y = 1

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

=> -12 - 2y + 2y = 1

=> -12 = 1

which is not possible.

**It is not possible to solve the given equations for any x and y.**

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.**