In which quadrant does the solution of the system fall?
x+y=4
2x-y=2
To determine in which quadrant the solution of the system falls, we need to solve the system of equations.
First, let's solve the system by the method of substitution:
Substitute the value of y from the first equation into the second equation:
2x - (4-x) = 2
2x - 4 + x = 2
3x - 4 = 2
3x = 6
x = 2
Substitute the value of x back into the first equation to solve for y:
2 + y = 4
y = 2
So the solution to the system is (x,y) = (2, 2).
Now, let's plot this point on a Cartesian coordinate system. The point (2,2) falls in the first quadrant, where both x and y values are positive.
Therefore, the solution of the system falls in the first quadrant.