Answer :
Answer:
The ordered pair (5,-6) is a solution to the first equation because it makes the first equation true
The ordered pair (5 - 6) is a solution to the second equation because it makes the second equation true
The ordered pair (5 - 6) is a solution to the system because it makes both equations true
Step-by-step explanation:
we have
[tex]x+y=-1[/tex] --- equation A
[tex]3x-y=21[/tex] ----> equation B
we know that
If a ordered pair is a solution of the system of equations, then the ordered pair must satisfy both equations
Solve the system of equations by elimination
Adds equation A and equation B
[tex]x+y=-1\\3x-y=21\\-----\\x+3x=-1+21\\4x=20\\x=5[/tex]
Find the value of y
substitute the value of x in any equation
[tex]x+y=-1[/tex]
[tex]5+y=-1[/tex]
[tex]y=-6[/tex]
The solution of the system is the point (5,-6)
therefore
Verify each statement
a) The ordered pair (5,-6) is a solution to the first equation because it makes the first equation true.
The statement is true (see the procedure)
b) The ordered pair (5 - 6) is a solution to the second equation because it makes the second equation true
The statement is true (see the procedure)
c) The ordered pair (5 - 6) is not a solution to the system because it makes at least one of the equations false
The statement is false (see the procedure)
d) The ordered pair (5 - 6) is a solution to the system because it makes both equations true
The statement is true (see the procedure)