Question

How many solutions does the system of equations below have? y = –10 7 x + 2 9 y = –10 7 x + 2 9

Answer 1

Infinitely many solutions.

Explanation:

Given

`y = -(10)/(7)x + (2)/(9)`

`y = -(10)/(7)x + (2)/(9)`

Required

Number of solutions

Substitute
`y = -(10)/(7)x + (2)/(9)` in the second equation

`-(10)/(7)x + (2)/(9) = -(10)/(7)x + (2)/(9)`

Add
`-(10)/(7)x` to both sides

`(10)/(7)x -(10)/(7)x + (2)/(9) = (10)/(7)x -(10)/(7)x + (2)/(9)`

`(2)/(9) = (2)/(9)`

The above solution implies that, the equations have infinitely many solutions.