Does the system have one solution, no solution, or infinitely many? Use your substitution to justify your answer

x+2y = - 10

-x+2y = - 2

Answer: 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