in which quadrant does the solution of the system fall?
x + y = 4
2x - y = 2
To find in which quadrant the solution of the system of equations falls, we first need to solve it to find the coordinates (x, y) of the solution. Let's solve the system of equations step by step:
1. x + y = 4
2. 2x - y = 2
You can solve this system using the substitution method, elimination method, or any other method you find convenient. Here, we'll use the elimination method by adding the two equations together to eliminate y:
(1) + (2):
(x + y) + (2x - y) = 4 + 2
3x = 6
Now, divide both sides by 3 to find x:
3x / 3 = 6 / 3
x = 2
Now that we have the value of x, we can substitute into either of the original equations to find y. Let's use equation (1):
x + y = 4
2 + y = 4
y = 4 - 2
y = 2
The solution to the system of equations is (x, y) = (2, 2).
Now, determining the quadrant:
Quadrant I: x > 0 and y > 0
Quadrant II: x < 0 and y > 0
Quadrant III: x < 0 and y < 0
Quadrant IV: x > 0 and y < 0
Since both x and y are positive (2, 2), the solution falls in Quadrant I.