Methods for systems.What is the best method to solve the system : substitution or elimination x-y=6 -2x+2y=1
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
Since the slopes of the lines are equal, the lines are parallel.
The system has no solution, since the lines have no intercepting point.