Question

Determine which system below will produce infinitely many solutions.

2x + 5y = 24
2x + 5y = 42
3x − 2y = 15
6x + 5y = 11
4x − 3y = 9
−8x + 6y = −18
5x − 3y = 16
−2x + 3y = −7

Answer 1

Its option c

Explanation:

Answer 2

The system of equations are
`4x-3y=9\hfill (1)`

`-8x+6y=-18\hfill (2)`

Equations (1) and (2) are same and these two given equations represents the same line.

Therefore the given system is consistent and it has an infinite number of solutions, and also it is dependent

Explanation:

Given system of equations is
`4x-3y=9\hfill (1)`

`-8x+6y=-18\hfill (2)`

To verify that the given system of equations have infinitely many solutions :

Equation (1) is
`4x-3y=9`

Equation (2) becomes

`2(-4x+3y)=2(-9)`

`-2(4x-3y)=-2(9)`

Dividing by (-2) on both sides we get

`4x-3y=9`

Therefore Equations (1) and (2) are same and these two given equations represents the same line.

Therefore the given system is consistent and it has an infinite number of solutions, and also it is dependent