Question
y>−x−1
y, is greater than, one third, x, minus, 5
y>
3
1
x−5
y, is greater than, one third, x, minus, 5
y>
3
1
x−5
Answers
Answered by
GPT-5 mini
Do you mean the system
y > −x − 1
and
y > (1/3)x − 5 ?
If so, the solution is all points (x,y) that satisfy both inequalities — i.e. all points above both lines. Equivalently
y > max(−x − 1, (1/3)x − 5).
Key facts:
- Line 1: y = −x − 1 (slope −1, y‑intercept −1).
- Line 2: y = (1/3)x − 5 (slope 1/3, y‑intercept −5).
- They intersect when −x − 1 = (1/3)x − 5. Solve:
(−4/3)x = −4 ⇒ x = 3, and y = −4. Intersection point: (3, −4).
To graph:
- Draw both lines as dashed (strict >).
- Shade the region above each line.
- The solution is the overlapping shaded region (points above the higher of the two lines). For x < 3 the line y = −x − 1 is higher; for x > 3 the line y = (1/3)x − 5 is higher.
If you meant something different, tell me and I’ll adjust.
y > −x − 1
and
y > (1/3)x − 5 ?
If so, the solution is all points (x,y) that satisfy both inequalities — i.e. all points above both lines. Equivalently
y > max(−x − 1, (1/3)x − 5).
Key facts:
- Line 1: y = −x − 1 (slope −1, y‑intercept −1).
- Line 2: y = (1/3)x − 5 (slope 1/3, y‑intercept −5).
- They intersect when −x − 1 = (1/3)x − 5. Solve:
(−4/3)x = −4 ⇒ x = 3, and y = −4. Intersection point: (3, −4).
To graph:
- Draw both lines as dashed (strict >).
- Shade the region above each line.
- The solution is the overlapping shaded region (points above the higher of the two lines). For x < 3 the line y = −x − 1 is higher; for x > 3 the line y = (1/3)x − 5 is higher.
If you meant something different, tell me and I’ll adjust.