Question

Hich equation can pair with x-y=-2 to create a consistent and dependent systems?

Answer 1

The equation that will create a consistent and dependent system is:

`-3x+3y=6`

Explanation:

The system of equations is consistent and dependent ( i.e. it will lead to infinite many solutions) is when the two equations represent the same line.

i.e. the two equations are similar.

The equation that satisfies this condition is:

`-3x+3y=6`

i.e. on dividing both side of the equation by 3 we get:

`-x+y=2`

On multiplying both side of the equation by "-1" we get:

`x-y=-2`

i.e. the two equations are similar.

• Hence, the two lines will coincide and so we will get infinite many solution (since each point on the line is the solution )

Answer 2

We can simplify each equation and find the solution.

6x + 2y = 15 can't be simplified further.

- 8x - 3y = 2 can't be simplified further.

4x - 4y = 6 on simplification gives 2x - 2y = 3 or x - y = 3/2

But, it does not coincide with the given equation.

- 3x + 3y = 6 on simplification gives x - y = - 2 coincides with the given equation.

Hence, - 3x + 3y = 6 can pair with x - y = -2 to create a consistent and dependent system.