Question

Use the substitution method to solve the following system of linear equations:

x + y = 6
x = –y + 2

Answer 1

there is There is no solutions. correct?

Answer 2

A.
The solution is (4, 2).

B.
There is no solution.

C.
The solution is (2, 4).

D.
There are an infinite number of solutions.

Answer 3

yeah, i think you are right, no solutions :)

Answer 4

thank you! :)

Answer 5

if you re-write the second equation
x + y = 6
x = –y + 2

to
x + y = 6
x +y = 2

you are looking for two numbers that when you add them, you get 6 and *at the same time* add up to 2

there are no numbers that can do that. so there is no solution.

Answer 6

Thank you @phi

Answer 7

or, if you rewrite both equations like this
x + y = 6
x = –y + 2

to

y = -1x +6
y = -1x + 2

you have the equation of two lines that have the same slope. they are parallel and *never meet*
the solution of these two equations is where the lines intersect... but in this case, they never intersect... so no solution.