Question

Which statements are true about the ordered pair (-1, -4) and the system of equations?

Answer 1

The given equations are

`x-y=3\text{ and }7x-y=-2.`

The given point is (-1,-4)

`\text{Substituting x=-1 and y=-4 in }x-y=3\text{ as follows:}`

`(-1)-(-4)=3`

`-1+4=3`

`3=3`

This equation is true.

When (-1,-4), substituted into the first equation, the equation is true.

The second option is correct.

`\text{Substituting x=-1 and y=-4 in 7}x-y=-2\text{ as follows:}`

`7(-1)-(-4)=-2`

`-7+4=-2`

`-3=-2`

This equation is not true.

When (-1,-4), substituted into the second equation, the equation is false.

The third option is correct.

If the ordered pair (-1,-4) is a solution to the system of linear equations, it should satisfy both linear equations.

When (-1,-4), substituted into the second equation, It does not satisfy this equation.

Hence the ordered pair (-1,-4) is not a solution to the system of linear equations.

Correct options are two, three and six.