Question

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

3x+4y=182x−2y=23x+4y=182x−2y=2

Select each correct answer.

When (2, 3) is substituted into the first equation, the equation is false.

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

When (2, 3) is substituted into the first equation, the equation is true.

When (2, 3) is substituted into the second equation, the equation is false.

When (2, 3) is substituted into the second equation, the equation is true.

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

Answer 1

When
`(2, 3)` is substituted into the first equation, the equation is true

When
`(2, 3)` 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

Explanation:

we have

`3x + 4y = 18` --------> First equation

`2x - 2y = 2` --------> Second equation

we know that

If a ordered pair is a solution of a system of linear equations

then

the ordered pair must be satisfy the first and the second equation of the system of linear equations

Statements

case A) When
`(2, 3)` is substituted into the first equation, the equation is false

The statement is false

Substitute the value of x and the value of y of the point
`(2, 3)` in the first equation

`3(2) + 4(3) = 18`

`18 = 18` -------> is true

therefore

the point
`(2, 3)` is a solution of the first equation

case B) The ordered pair
`(2, 3)` is a solution to the system of linear equations

The statement is false

Because, the ordered pair
`(2, 3)` is not a solution of the second equation

Verify

Substitute the value of x and the value of y of the point
`(2, 3)` in the second equation

`2(2) - 2(3) = 2`

`-2 = 2` ------> is not true

therefore

the ordered pair
`(2, 3)` is not a solution of the second equation

case C) When
`(2, 3)` is substituted into the first equation, the equation is true

The statement is true

Substitute the value of x and the value of y of the point
`(2, 3)` in the first equation

`3(2) + 4(3) = 18`

`18 = 18` -------> is true

therefore

the point
`(2, 3)` is a solution of the first equation

case D) When
`(2, 3)` is substituted into the second equation, the equation is false

The statement is true

Substitute the value of x and the value of y of the point
`(2, 3)` in the second equation

`2(2) - 2(3) = 2`

`-2 = 2` ------> is not true

case E) When
`(2, 3)` is substituted into the second equation, the equation is true

The statement is false

Substitute the value of x and the value of y of the point
`(2, 3)` in the second equation

`2(2) - 2(3) = 2`

`-2 = 2` ------> is not true

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

The statement is true

Because, the ordered pair
`(2, 3)` is not a solution of the second equation

Answer 2

3x + 4y = 18......(2,3)
3(2) + 4(3) = 18
6 + 12 = 18
18 = 18...correct

2x - 2y = 2....(2,3)
2(2) - 2(3) = 2
4 - 6 = 2
-2 = 2...incorrect

when (2,3) is subbed into equation 1, it is true
when (2,3) is subbed into the second equation, it is false
the ordered pair (2,3) is not a solution to the system of linear equations