Question

HELP PLEASE

The statement explains why the ordered pair is a solution to the system of equations. Is the statement true or false?
The ordered pair (−4,−1) is a solution to the system of equations because when​ ​(−4,−1)​ is substituted into the equation, both equations are true.
​3x+8y=20
−5x+y=19
True or False?

Answer 1

False

Explanation:

Given : The ordered pair (−4,−1) is a solution to the system of equations because when​ ​(−4,−1)​ is substituted into the equation, both equations are true.
`3x+8y=20` and
`-5x+y=19`

To find : Is the statement true or false?

Solution :

Let the equations,

`3x+8y=20` .....Equation (1)

`-5x+y=19` .......Equation (2)

Now, We have to determine that (-4,-1) is a solution of equations or not.

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

`3x+8y=20`

`3(-4)+8(-1)=20`

`-12-8 = 20`

`-20= 20`

False, The point is not satisfied the equation.

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

`-5x+y=19`

`-5(-4)+(-1)=19`

`20-1 = 19`

`19=19`

True, The point is satisfied the equation.

Since, The statement given is not true as ordered pair(-4,-1) is not satisfying the equation.

Therefore, The answer is false.

Answer 2

False,

(-4, -1) is not a solution of the given system of equations

Explanation:

Given the system of equations:

`3x+8y =20` .......[1]

`-5x+y =19` ......[2]

To determine (-4, -1) is a solution

Substitute x = -4 and y = -1 in both the equations, if they both satisfied then it is a solution.

`3(-4)+8(-1)=20`

⇒
`-12-8 = 20`

⇒
`-20 = 20` False.

`-5(-4)+(-1)=19`

⇒
`20-1 = 19`

⇒
`19=19` True.

Since, the given statement is not true

because the ordered pair (-4, -1) does not satisfy the given system of equations.