 Enrol now for our new online tutoring program. Learn from the best tutors. Get amazing results. Learn more.

August 02, 2021, 12:00:12 pm

### AuthorTopic: Maths Graphs  (Read 363 times) Tweet Share

0 Members and 1 Guest are viewing this topic.

#### biology1234

• Trailblazer
• • Posts: 35
• Respect: 0 ##### Maths Graphs
« on: June 15, 2021, 10:56:07 pm »
0
Use a graph to show the solution to the following pair of simultaneous inequalities.
y > 3x-3
3y +5x =15 < or equal to 0

Could someone attach the final solution graph, to guide me. Thanks

#### fun_jirachi

• MOTM: AUG 18
• HSC Moderator
•     • • Posts: 983
• All doom and Gloom.
• Respect: +658 ##### Re: Maths Graphs
« Reply #1 on: June 15, 2021, 11:27:11 pm »
+2
Attaching the graph with the solution is a little redundant if you actually want to learn. Here are a few hints you can use to construct your own graph instead:

- Instead of graphing the inequality, graph the equality first. For example, if you had $y > 3x-3$, graph $y = 3x-3$.
- Test some points on either side of the curve. For example, we could test the point $(0, 3)$. Here, we can clearly see that $y$ is indeed greater than $3x-3$. This means that the side of the curve that contains $(0, 3)$ is the side where the inequality holds true. Shade this area in. Conversely, a point such as $(0, -4)$ would not work - implying that the inequality does not hold true for that side of the curve.

Repeat for the other curve; the intersection of the two shaded areas is the final shaded area that should be left. Note that for strict inequalities the convention is that the curve is marked by a dotted line (to show exclusion), while for non-strict inequalities, the convention is that the curve is marked by a solid line (to show inclusion).
Spoiler
HSC 2018: Mod Hist  | 2U Maths 
HSC 2019: Physics  | Chemistry  | English Adv  | 3U Maths  | 4U Maths 
ATAR: 99.05

UCAT: 3310 - VR  | DM  | QR  | AR