Question

Please Answer Quick 70 Points !

Which statements are true about the ordered pair (7, 19) and the system of equations?

{2x−y=−5x+3y=22


Select each correct answer.

The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.
The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (7, 19) is a solution to the system because it makes both equations true.

Answer 1

The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true

The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false

Explanation:

we have

`2x-y=-5` -----> First equation

`x+3y=22` -----> Second equation

Solve the system of equations by graphing

Remember that the solution of the system is the intersection point both graphs

The solution is the point (1,7)

The ordered pair (7,19) lie on the first line, so is a solution of the first equation

see the attached figure

Verify each statement

case 1) The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true

The statement is true

case 2) The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true

The statement is false, because the ordered pair (7,19) not lie on the second line

case 3) The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false

The statement is true

case 4) The ordered pair (7, 19) is a solution to the system because it makes both equations true

The statement is false,because it makes only the first equation true