Question

The solution to the system of equation below is (−2, −1).

2x − 3y = −1
11x − 9y = −13

When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.

Which system of equations will also have a solution of (−2, −1)?


5x = −10
11x − 9y = −13


2x + 9y = −1
11x − 9y = −13


−6x + 9y = −1
11x − 9y = −13


−6x + 3y = −1
5x = −10

Answer 1

5x=-10
11x-9y=-13

5x(-2)=-10
11x(-2)-9x(-1)=-13

Answer 2

The correct option is 1.

Explanation:

If a system of equation have solution (a,b), then the equations of system must be satisfied by the point (a,b).

It is given that the system of have solution (-2,-1), so the equations of system must be satisfied by the point (-2,-1).

The system of equation in option 1 is

`5x=-10`

`11x-9y=-13`

Put (-2,-1) in the above equations.

`5(-2)=-10\Rightarrow -10=-10`

`11(-2)-9(-1)=-13\Rightarrow -13=-13`

Since left hand side is equal to right hand side, therefore the point (-2,-1) satisfy the equations and (-2,-1) is the solution of the given system.

Similarly check the other system of equations, whether the point (-2,-1) stratify the equations or not.

In option 2,

`2x+9y=-1`

`2(-2)+9(-1)=-1\Rightarrow -13=-1`

Since left hand side is not equal to right hand side, therefore the point (-2,-1) is not the solution of this system of equation.

In option 3,

`-6x+9y=-1`

`-6(-2)+9(-1)=-1\Rightarrow 3=-1`

Since left hand side is not equal to right hand side, therefore the point (-2,-1) is not the solution of this system of equation.

In option 4,

`-6x+3y=-1`

`-6(-2)+3(-1)=-1\Rightarrow 9=-1`

Since left hand side is not equal to right hand side, therefore the point (-2,-1) is not the solution of this system of equation.

Only option 1 is correct.