Question

Which point would be a solution to the system of linear inequalities shown below?
y, is greater than or equal to, one half, x, plus, 1, y, is less than, minus, start fraction, 3, divided by, 2, end fraction, x, plus, 5
y≥
2
1
​
x+1y<−
2
3
​
x+5
Answer
Multiple Choice Answers
left parenthesis, minus, 4, comma, minus, 5, right parenthesis(−4,−5)
left parenthesis, 4, comma, minus, 4, right parenthesis(4,−4)
left parenthesis, 4, comma, 5, right parenthesis(4,5)
left parenthesis, minus, 12, comma, minus, 4, right parenthesis(−12,−4)

Answer 1

Check each point in y ≥ (1/2)x + 1 and y < −(3/2)x + 5.

For (−12, −4):
- (1/2)(−12) + 1 = −6 + 1 = −5, and −4 ≥ −5 ✓
- −(3/2)(−12) + 5 = 18 + 5 = 23, and −4 < 23 ✓

So (−12, −4) satisfies both inequalities. Answer: (−12, −4).