Question

select the correct answer.
for which system of inequalities is (3,-7) a solution?
a. x + y < -4
3x + 2y < -5
b. x + y ≤ -4
3x + 2y < -5
c. x + y < -4
3x + 2y ≤ -5
d. x + y ≤ -4
3x + 2y ≤ -5

Explanation:

Step1: Substitute \(x = 3\), \(y=-7\) into \(x + y\)

Calculate \(x + y\): \(3+(-7)=3 - 7=-4\)

Step2: Substitute \(x = 3\), \(y = -7\) into \(3x+2y\)

Calculate \(3x + 2y\): \(3\times3+2\times(-7)=9-14=-5\)

Step3: Check each option

• Option A: \(x + y=-4\) which is not less than \(-4\), and \(3x + 2y=-5\) which is not less than \(-5\), so A is wrong.
• Option B: \(x + y=-4\) satisfies \(x + y\leq - 4\), but \(3x + 2y=-5\) is not less than \(-5\), so B is wrong.
• Option C: \(x + y=-4\) is not less than \(-4\), and \(3x + 2y=-5\) satisfies \(3x + 2y\leq - 5\), so C is wrong.
• Option D: \(x + y=-4\) satisfies \(x + y\leq - 4\), and \(3x + 2y=-5\) satisfies \(3x + 2y\leq - 5\), so D is correct.

Answer:

D. \(x + y\leq - 4\); \(3x + 2y\leq - 5\)