Maths Graphs

[biology1234]

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]

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).