Question

Which statements are true about the ordered pair (-1,-4) and the system of equations?

x-y=3

7x-y=-3

Question 1 options:


When (-1,-4) is substituted into the first equation, the equation is false.


When (-1,-4) is substituted into the first equation, the equation is true.


When (-1,-4) is substituted into the second equation, the equation is false.


When (-1,-4) is substituted into the second equation, the equation is true.


The ordered pair (-1,-4) is a solution to the system of linear equations


The ordered pair (-1,-4) is not a solution to the system of linear equations.

Answer 1

1.When (-1,-4) is substituted into the first equation, the equation is false. FALSE

2. When (-1,-4) is substituted into the first equation, the equation is true. TRUE

3. When (-1,-4) is substituted into the second equation, the equation is false.

FALSE

4. When (-1,-4) is substituted into the second equation, the equation is true. TRUE

5.The ordered pair (-1,-4) is a solution to the system of linear equations .TRUE

6.The ordered pair (-1,-4) is not a solution to the system of linear equations.

FALSE

Explanation:

Here, the given set if equations are:

x - y = 3

7 x - y = - 3

Now, substituting the given value (-1,-4) in the given equations, we get

(1) Substitute (-1, -4) in first equation:

x - y = 3 : (-1, -4)

⇒ (-1) - (-4) = -1 + 4 = 3 = Right Side

So, the equation x - y = 3 holds TRUE for (-1,-4)

(2) Substitute (-1, -4) in second equation:

7 x - y = - 3 : (-1, -4)

⇒ 7(-1) - (-4) = -7 + 4 = -3 = Right Side

So, the equation 7 x - y = - 3 holds TRUE for (-1,-4)

Now, the given options are:

When (-1,-4) is substituted into the first equation, the equation is false. FALSE, equation is satisfied.

When (-1,-4) is substituted into the first equation, the equation is true.

TRUE

When (-1,-4) is substituted into the second equation, the equation is false.

FALSE, the given equation is satisfied.

When (-1,-4) is substituted into the second equation, the equation is true.

TRUE

The ordered pair (-1,-4) is a solution to the system of linear equations .

TRUE,as the given point satisfies both the equations.

The ordered pair (-1,-4) is not a solution to the system of linear equations.

FALSE,as the given point satisfies the equation.