Answer:
Option C
Step-by-step explanation:
We solve the system of equations by using the Elimination method as follows,
[tex]2x-5y=-5\\x+2y=11\\[/tex]
We multiply the second equation with -2 and then add both the equations to eliminate the variable x
[tex]-2(x+2y=11) \\-2x-4y=-22[/tex]
so now,
[tex]2x-5y=-5\\-2x-4y=-22\\2x+(-2x)-5y+(-4y)=-5+(-22)\\2x-2x-5y-4y=-5-22\\0-9y=-27\\-9y=-27\\y=-27/-9\\y=3[/tex]
we found the value of y to be y = 3 now we insert this value in any equation of the system either it be the first or the second to calculate the value of x so here goes,
[tex]x+2y=11\\x+2(3)=11\\x+6=11\\x=11-6\\x=5\\[/tex]
so the solution to the system of equations is (5 , 3) not (10 , 5) which is given in the question even though the ordered pair (10 , 5) satisfies the first equation it is not the solution to the system because in the system it has two equations instead of one so (10 , 5) holds true for the first equation not for the second so Option C is your best answer because it atleast makes one of the equations false.
