In which quadrant does the solution of the system fall?

x + y = 4

Answer 1

From X + Y = 4
Y = 4 – X
Substituite this for Y in 2X – Y = 2 to get
2X -(4 – X ) = 2
2X -4 +X = 2
3X = 6
X = 2
Now return to X + Y = 4
Knowing X = 2,
2 + Y = 4
Y = 4 – 2
Y = 2
The solution is (X,Y) = (2,2)
This is quadrant I
Answer is A

Answer 2

Look at the first equation. If x + y = 4, that means x = 4 – y. We can now substitute that in for x in the second equation.

2x – y = 2
2*(4-y) – y = 2
8 – 2y – y = 2
8 – 3y = 2
-3y = – 6
y = 2

And since we know x + y = 4, x = 2. So the solution is (2,2), which is in quadrant 1.

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