Question

Which statements are true about the ordered pair (−1, 5) and the system of equations?

Answer 1

Answer:

Option D is correct answer.

Step-by-step explanation:

We are given the system of equations:

$x+y=4\\x-y=-6$

Solving the system of equations to find values of x and y

Let:

$x+y=4--eq(1)\\x-y=-6--eq(2)$

Adding both equations to find value of x

$x+y=4\\x-y=-6\\------\\2x=-2\\x=\frac{-2}{2}\\x=-1$

So, we get value of x: x=-1

Now, putting value of x: x=-1 into equation 1 to find value of y

$x+y=4\\Putx=-1\\-1+y=4\\y=4+1\\y=5$

So, we get value of y: y=5

The ordered pair will be: (-1,5)

So, Option D: The ordered pair(-1,5) is a a solution to the system of equations because it makes both equations true is correct choice.

Checking:

Put x=-1 and y=5 in equation 1

$x+y=4\\-1+5=4\\4=4\:True$

Put x=-1 and y=5 in equation 2

$x-y=-6-1-5=-6\\-6=-6\:\:\:True$

So, both equations are true.

Therefore, Option D is correct answer.