solve the system of equations using the addition elimination method.If the answer is a uniique solutio?

Question

present it as an order pair :(x,y). if not, specifiy whether the answer is no solution or infinitely many soloutions.
-7x + y = 8
2x - y = 2

Answer 1

Elimination by addition method

-7x + y = 8- - - - - -Equation 1
2x - y = 2- - - - - - -Equation 2
- - - - - - - - -
- 5x = 10

- 5x / - 5 = 10 / - 5

x = 10/- 5

x = - 2

Insert the x value into equation 1
- - - - - - - - - - -

- 7x + y = 8

- 7(- 2) + y = 8

- ( - 14) + y = 8

14 + y = 8

14 + y - 14 = 8 - 14

y = - 6

Insert the y value into equation 1
- - - - - - - -

Check for equation 1

- 7x + y = 8

- 7(- 2) + ( - 6) = 8

- (- 14) - 6 = 8

14 - 6 = 8

8 = 8

- - - - - - -

Check for equation 2

2x - y = 2

2(- 2) - ( - 6) = 2

- 4 + 6 = 2

2 = 2

- - - - - - - - -

Both equations balance

The solutiion set { - 2, - 6 }

- - - - - - - -s-

Answer 2

Add the 2 equations together to get

-7x + y = 8
2x - y = 2
------------------
-5x = 10
x = -2

Plug this value of x into one of the equations

2(-2) - y = 2
-4 - y = 2
y = -6

so x = -2 and y = -6

Answer 3

x=-2, y=-6

Answer 4

Add the 2 equations and you get
-5x=10
x=-2
put this into second equation
-4-y=2
y=-6