In which quadrant does the solution of the system fall?

Question

x + y = 4
2x - y = 2

A.) I

B.) II

C.) III

D.) IV

Answer 1

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.