The solution for the system of equation is option (B) (2,-5) is the correct answer.
A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.
For the given situation,
The system of equations are
3x – 4y = 26 -------- (1)
2x + 8y = –36 --------(2)
Now multiply equation 1 by 2,
⇒ [tex]6x-8y=52[/tex] --------- (3)
Now multiply equation 2 by 3,
⇒ [tex]6x+24y=-108[/tex] --------- (4)
Subtract equation 4 from equation 3, we get
⇒ [tex]-32y=160[/tex]
⇒ [tex]y=-5[/tex]
Substitute y = -5 in equation 1,
⇒ [tex]3x-4(-5)=26[/tex]
⇒ [tex]3x=26-20[/tex]
⇒ [tex]3x=6[/tex]
⇒ [tex]x=2[/tex]
Hence we can conclude that the solution for the system of equation is option (B) (2,-5) is the correct answer.
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