Question

Which statements are true the ordered pair (1, 2) and the system of equations?

y = -2x + 4
7x - 2y = 3
Select each correct answer.

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

Answer 1

The ordered pair (1, 2) satisfies both equations in the system, making it a solution to the system of linear equations. The statements that the ordered pair makes both equations true are correct.

Step-by-step explanation:

To determine which statements are true regarding the ordered pair (1, 2) and the system of equations y = -2x + 4 and 7x - 2y = 3, we need to substitute the values of the ordered pair into each equation and check for validity.

Substituting (1, 2) into the first equation:

1. y = -2x + 4
2. 2 = -2(1) + 4
3. 2 = -2 + 4
4. 2 = 2 (true)

Substituting (1, 2) into the second equation:

1. 7x - 2y = 3
2. 7(1) - 2(2) = 3
3. 7 - 4 = 3
4. 3 = 3 (true)

Since the ordered pair satisfies both equations, it is indeed a solution to the system of linear equations. Therefore, the following statements are true:

• When (1, 2) is substituted into the first equation, the equation is true.
• When (1, 2) is substituted into the second equation, the equation is true.
• The ordered pair (1, 2) is a solution to the system of linear equations.