Question

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

Answer 1

Answer:

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

Step-by-step 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