Does the system have one solution, no solution, or infinitely many? use your substitution to justify your answerx+2y= -10-x+2y= -2

It has one solution. The solution is (x,y) = (-4,-3)

Add up the equations doing so straight down

x + -x = 0x = 0 so the x terms go away

2y + 2y = 4y

-10 + (-2) = -12

We end up with 4y = -12 so y = -3 after you divide both sides by 4. Use this y value to find the value of x

x+2y = -10

x + 2(-3) = -10

x - 6 = -10

x = -10+6

x = -4

The single solution is (x,y) = (-4,-3)

As a check, plug this solution into each equation to see if you get a true statement or not. Let's do so with the first equation

x+2y = -10

-4 + 2(-3) = -10

-4 - 6 = -10

-10 = -10 true

and then the second equation

-x+2y = -2

-(-4) + 2(-3) = -2

4 - 6 = -2

-2 = -2 true

both equations are true, so the solution is confirmed

think about it deeply and passionately about this property

i am sorry

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d