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Given:
The system of equation is
[tex]y=-8x-3[/tex]
[tex]x+y=7[/tex]
To find:
Whether (3,4) is a solution of the given system or not.
Solution:
We have,
[tex]y=-8x-3[/tex] ...(i)
[tex]x+y=7[/tex] ...(ii)
Putting the value of y in (ii) from (i), we get
[tex]x+(-8x-3)=7[/tex]
[tex]x-8x-3=7[/tex]
[tex]-7x=7+3[/tex]
[tex]-7x=10[/tex]
Divide both sides by -7.
[tex]x=\dfrac{10}{-7}[/tex]
[tex]x=-\dfrac{10}{7}[/tex]
Putting [tex]x=-\dfrac{10}{7}[/tex] in (i), we get
[tex]y=-8\times (\dfrac{-10}{7})-3[/tex]
[tex]y=\dfrac{80}{7}-3[/tex]
[tex]y=\dfrac{80-21}{7}[/tex]
[tex]y=\dfrac{59}{7}[/tex]
So, the only solution of the given system is [tex]\left(-\dfrac{10}{7},\dfrac{59}{7}\right)[/tex].
Hence, (3,4) cannot be a solution of given system, Hence the correct option is B.
Answer: B I got it right in khan academy
Step-by-step explanation: