Question

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Answer 1

multiply the first equation by -2 to get: -2x - 2y = -6
if you add the first and second equations together:
-2x - 2y = -6
+ 2x + 2y = 10
________________
0x + 0x = 4
since that's impossible, the answer is c: No solutions.

Another way to solve it is to substitute: y = 3 - x
so 2x + 2(3 - x) = 10
2x + 6 - 2x = 10
6 = 10
not possible. so no solutions.

Answer 2

Easier one to understand:
multiply the first by 2
2x+2y=6
2x+2y=10
subtract
0=-4
No they don't so there is no solution.
They are parallel.
y=-x+3
divide the second by 2


x+y=5
y=-x+5
they have the same slope (-1)
I didn't use substitution.
x=3-y
2(3-y)+2y=10
6-2y+2y=10
6=10
no they don't
there is no solution