Question

Can someone please help me on this one!

Answer 1

Answer:

The answer is (1,-1)

Step-by-step explanation:

The best approach for this problem is to plug in the coordinates into the given inequality.

$7x-3y\geq 10$

(3,4) ------> $7(3)-3(4)=9$

9 is less than 10 so, we can rule this one out.

(1,0) -------> $7(1)-3(0)=7$

7 is less than 10 so, we can rule this one out.

(1,2) -------> $7(1)-3(2)=1$

1 is less than 10 so, we can rule this one out.

(1,-1) -------> $7(1)-3(-1)=10$

10 is equal to 10, so this is the answer.

Hope this helps!

Answer 2

As mentioned by Mark there are an unlimited number of pairs that satisfy your equation. So let us see how you can characterize these solutions

if 7x - 3y > 10 then

7x > 10 +3y

Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6

then by substitution

7  must be > 10+ 3*6

or 7x must be > 28

or x must be > 4

So all pairs such that x is > 4 and y = 6 are solutions.

I can create an infinite number of pairs choosing any number for y. Likewise I could have chosen x and solved the problem for y. In the above example I chose 6 for y to make the division easy. I could have chosen any number(real or integer) for y and solved the equation for x  to derive appropriate  pairs