How do you graph the inequality 5x+y>105x+y>10?

2 Answers
Feb 13, 2017

Treat the inequality sign as an equal sign.

Explanation:

5x+y=105x+y=10

y=10-5xy=105x

Now, just pick your values for x and solve for y!

Feb 14, 2017

Please see below.

Explanation:

Let us first consider the equality i.e. 5x+y=105x+y=10

or y=10-5xy=105x

Now, just pick values for xx and solve for yy

Let us pick x=0,2x=0,2 and 44

As y=10-5xy=105x, y=10,0y=10,0 and -1010

and joining points (0,10)(0,10), (2,0)(2,0) and (4,-10)(4,10) we get following graph.
graph{10-5x [-20, 20, -10, 10]}
But this is still not the graph for 5x+y>105x+y>10

Observe that this line divides Cartesian plane in three parts.

Part 1 is the line itself and we know on the line 5x+y=105x+y=10 and hence line is not the solution.

Part 2 is the left hand side of the line. One point on the left is (0,0)(0,0) and if we put these values of xx and yy we get 00, which is less than 1010. Hence in Part 2, we have 5x+y<105x+y<10. This too is not a solution as what we need is 5x+y>105x+y>10.

Part 3 is the right hand side of the line. One point to the right is (5,0)(5,0) and if we put these values of xx and yy we get 2525, which is greater than than 1010. Hence in Part 2, we have 5x+y>105x+y>10 and this is the solution and it looks like
graph{5x+y>10 [-20, 20, -10, 10]}
Observe that line is dashed , which shows that points on the line do not form the solution.