Question

I need to figure out how many solutions does the system of equations below have.

y=6/7x-8 and y=7/9x+10/9

Answer 1

The system has one solution.

Explanation:

To find the number of solutions of the system, we equal both equations for y.

If we have ax = b, in which both a and b are different of 0, we have one solution.

If both a and b are 0, we have infinite solutions.

If a is 0 and b is not, there are no solutions.

y=6/7x-8 and y=7/9x+10/9

So

`(6x)/(7) - 8 = (7x)/(9) + (10)/(9)`

`(6x)/(7) - (7x)/(9) = (10)/(9) + 8`

`(54x - 49x)/(63) = (10)/(9) + (72)/(9)`

`(5x)/(63) = (82)/(9)`

`45x = 63*82`

Both a and b are different of 0, so the system has one solution.