In which quadrant does the solution of the system fall?
x + y = 4
2x – y = 2
To determine the quadrant in which the solution of the system falls, we need to solve the system of equations. Rewriting the second equation in terms of y, we have:
2x - y = 2
-y = -2x + 2
y = 2x - 2
Now, we can substitute this expression for y into the first equation:
x + y = 4
x + (2x - 2) = 4
3x - 2 = 4
3x = 6
x = 2
Substituting the value of x back into the second equation, we can find the corresponding y-coordinate:
y = 2x - 2
y = 2(2) - 2
y = 4 - 2
y = 2
Therefore, the solution to the system of equations is (2, 2). This point falls in the first quadrant of the coordinate plane.