Question

Which statements are true about the ordered pair (10, 5) and the system of equations?

{2x−5y=−5x+2y=11


Select each correct answer.


The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true.

The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true.

The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.

The ordered pair (10, 5) is a solution to the system because it makes both equations true.

Answer 1

C

Explanation:

We have the system of equations:

`\left\{\begin{array}{ll}2x-5y=-5 \\ x+2y=11\end{array}`

And an ordered pair (10, 5).

In order for an ordered pair to satisfy any system of equations, the ordered pair must satisfy both equations.

So, we can eliminate choices A and B. Satisfying only one of the equations does not satisfy the system of equations.

Let’s test the ordered pair. Substituting the values into the first equation, we acquire:

`2(10)-5(5)\stackrel{?}{=}-5`

Evaluate:

`20-25\stackrel{?}{=}-5`

Evaluate:

`-5\stackrel{\checkmark}{=} -5`

So, our ordered pair satisfies the first equation.

Now, we must test it for the second equation. Substituting gives:

`(10)+2(5)\stackrel{?}{=} 11`

Evaluate:

`20\\eq 11`

So, the ordered pair does not satisfy the second equation.

Since it does not satisfy both of the equations, the ordered pair is not a solution to the system because it makes at least one of the equations false.

Therefore, our answer is C.