In which quadrant does the solution of the system fall?
x + y = 4
2x - y = 2
A.) I
B.) II
C.) III
D.) IV
To determine the quadrant in which the solution of the system falls, we need to solve the system of equations.
x + y = 4
2x - y = 2
We can solve this system by substitution or elimination. Let's use elimination:
Multiply the first equation by 2 to match the coefficients of y:
2x + 2y = 8
2x - y = 2
Now subtract the second equation from the first:
(2x + 2y) - (2x - y) = 8 - 2
3y = 6
y = 2
Substitute this value of y back into the first equation:
x + y = 4
x + 2 = 4
x = 2
So, the solution of the system is x = 2 and y = 2.
Since both x and y are positive, the solution falls in the first quadrant.
Therefore, the answer is A.) I.