Solve the system of equations using the substution method?

Question

1)
x-5y=32
-3x=y

2)
x-y=8
3x+2y=-1

Thanks in advance!

THANK YOU SOOOOO MUCH!

Answer 1

Question 1
x - 5 (- 3x) = 32
x + 15x = 32
16x = 32
x = 2
y = - 6

Question 2
x = 8 + y
24 + 3y + 2y = - 1
5y = - 25
y = - 5

x + 5 = 8
x = 3

Answer 2

1)
Value of y:
x - 5y = 32
5y = x - 32
y = (x - 32)/5

Value of x:
(x - 32)/5 = - 3x
x - 32 = - 15x
16x = 32
x = 2

Value of y:
= - 3(2)
= - 6

Answer: x = 2, y = - 6

Proof:
2 - 5(- 6) = 32
2 + 30 = 32

2)
Values of y:
x - y = 8
y = x - 8

3x + 2y = - 1
2y = - 3x - 1
y = (- 3x - 1)/2

Value of x:
x - 8 = (- 3x - 1)
2x - 16 = - 3x - 1
5x = 15
x = 3

Value of y:
= 3 - 8
= - 5

Answer: x = 3, y = - 5

Proof:
3(3) + 2(- 5) = - 1
9 - 10 = - 1

Answer 3

x - 5(-3x) = 32
x + 15x = 32
16x = 32
x = 2

-3(2) = y
-6 = y

x = y + 8

3(y+8) + 2y = -1
3y + 24 + 2y = -1
5y = -25
y = -5

x = 5 + 8
x = 13

Answer 4

1)
x-5y=32 (eq.1)
-3x=y (eq.2)

substitute the value of y in eq. 1,

x - 5 (-3x) = 32

simplify,

x + 15 x = 32

16x = 32

divide to the coefficien of x, you get

x = 2


2)
x-y=8 (eq. 1)
3x+2y=-1 (eq. 2)

from eq.1 we have value of x in terms of y

x = y + 8

then substitute the x in eq. 2

3 (y + 8 ) + 2y= -1

simplify,

3y + 24 + 2y = -1

combining like terms,

3y + 2y = -1 - 24

5y = -25

divide to the coefficien of y, you get


y = -5

hope it helps.