Question

Which graph represents the solution set of the system of inequalities?

x+y<1
2y≥x−4
 
I think its the one in the top right corner (the highlighted one)

Answer 1

Solve first for the solution of the inequalities. This can be done by replacing first the inequalities sign with the equal sign.

x + y = 1
2y = x - 4

The values of x and y from the system of linear equation are 2 and -1. This means that the intersection of the lines should be at point (2, -1).

Substitute 3 to x and determine the value of y from the second inequality.
2y ≥ x - 4

Substituting,
2y ≥ 3 - 4, y ≥ -1/2

Hence, the solution to this item should be the fourth one.