50 points! 2 questions! solve the system of equations using the given methods. show your work.

63.y = -4 and x = 2

64. x = 3 and y = 5

Step-by-step explanation:

63.

We are given that

y = x - 6

x + y = -2

We need to use the substitution method, so let's find x in terms of y.

Adding 6 to both sides of the first equation, we get

x = 6 + y

Substituting 6 + y into the second equation, we get

(6 + y) + y = -2

2y + 6 = -2

2y = -8

y = -4

Now, solving for x, we get

x + (-4) = -2

x = 2

Checking our answer by substituting these into the first equation,

-4 = 2 - 6?

-4 = -4  

So that's all good

64.

x + y = 8

-x + 2y = 7

Adding the two equations together will eliminate the x variable, allowing us to solve for y. This is the addition/elimination method

3y = 15

y = 5

Putting y back into the first equation gives us

x + 5 = 8

x = 3

Checking our answer in the second equation, we get

-(3) + 2 (5) = 7?

-3 + 10 = 7?

7 = 7 :)

all work is pictured and shown

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0