Question

Which statements are true about the ordered pair (2, 3) and the system of equations?

3x+4y=182x−2y=2

Select each correct answer.

Responses

When (2, 3) is substituted into the first equation, the equation is false.
When , begin ordered pair 2 comma 3 end ordered pair, is substituted into the first equation, the equation is false.

The ordered pair (2, 3) is a solution to the system of linear equations.
The ordered pair , begin ordered pair 2 comma 3 end ordered pair, is a solution to the system of linear equations.

When (2, 3) is substituted into the first equation, the equation is true.
When , begin ordered pair 2 comma 3 end ordered pair, is substituted into the first equation, the equation is true.

When (2, 3) is substituted into the second equation, the equation is true.
When , begin ordered pair 2 comma 3 end ordered pair, is substituted into the second equation, the equation is true.

When (2, 3) is substituted into the second equation, the equation is false.
When , begin ordered pair 2 comma 3 end ordered pair, is substituted into the second equation, the equation is false.

The ordered pair (2, 3) is not a solution to the system of linear equations.

Answer 1

The ordered pair (2, 3) satisfies the first equation 3x + 4y = 18 when substituted, making it true, but it does not satisfy the second equation 2x - 2y = 2, thus making it false. Therefore, (2, 3) is not a solution to the system of linear equations.

Step-by-step explanation:

To determine if the ordered pair (2, 3) is a solution to the given system of equations, we substitute x = 2 and y = 3 into each equation and see if they satisfy both.

The first equation is 3x + 4y = 18. By substituting, we get:

• 3(2) + 4(3) = 6 + 12 = 18, which is true.

The second equation is 2x - 2y = 2. By substituting, we get:

• 2(2) - 2(3) = 4 - 6 = -2, which is false.

Given that the ordered pair satisfies the first equation but not the second, the correct statements are:

1. When (2, 3) is substituted into the first equation, the equation is true.
2. When (2, 3) is substituted into the second equation, the equation is false.
3. The ordered pair (2, 3) is not a solution to the system of linear equations.