Answer:
1) True
2) True
3) False
4) True
5 True
Step-by-step explanation:
1) y ≤ x - 3 and y ≥ -x - 2 ⇒ check if (3 , -2) is a solution of them
∵ -2 ≤ 3 - 3 ⇒ -2 ≤ 0 ⇒ true inequality
∵ -2 ≥ -3 - 2 ⇒ -2 ≥ -5 ⇒ true inequality
- Both of them are true
∴ (3 , -2) is a solution of y ≤ x - 3 and y ≥ -x - 2
∴ True
2) y > -3x + 3 and y > x + 2 ⇒ check if (1 , 4) is a solution of them
∵ 4 > -3(1) + 3 ⇒ 4 > 0 ⇒ true inequality
∵ 4 > 1 + 2 ⇒ 4 > 3 ⇒ true inequality
- Both of them are true
∴ (1 , 4) is a solution of y > -3x + 3 and y > x + 2
∴ True
3) y ≤ 3x - 6 and y > -4x + 2 ⇒ check if (0 , -2) is a solution of them
∵ -2 ≤ 3(0) - 6 ⇒ -2 ≤ 0 - 6 ⇒ -2 ≤ -6 ⇒ wrong inequality
∵ -2 > -4(0) + 2 ⇒ -2 > 0 + 2 ⇒ -2 > 2 ⇒ wrong inequality
- Both of them are wrong
∴ (0 , -2) is not a solution of y ≤ 3x - 6 and y > -4x + 2
∴ False
4) 2x - y < 4 and x + y > -1 ⇒ check if (0 , 3) is a solution of them
∵ 2(0) - (3) < 4 ⇒ 0 - 3 < 4 ⇒ -3 < 4 ⇒ true inequality
∵ (0) + 3 > -1 ⇒ 3 > -1 ⇒ true inequality
- Both of them are true
∴ (0 , 3) is a solution of 2x - y < 4 and x + y > -1
∴ True
5) y > 2x - 3 and y < -x + 6 ⇒ check if (-3 , 0) is a solution of them
∵ 0 > 2(-3) - 3 ⇒ 0 > -6 - 3 ⇒ 0 > -9 ⇒ true inequality
∵ 0 < -(-3) + 6 ⇒ 0 < 3 + 6 ⇒ 0 < 9 ⇒ true inequality
- Both of them are true
∴ (-3 , 0) is a solution of y > 2x - 3 and y < -x + 6
∴ True
