Use substitution method to find the solutions?

Question

{y= 1-x/3
{5x-6y= -2
AND
{3x-5y= -1
{x+2y= 18

Thank you for your help!

Answer 1

the first one...

y=1-x/3
5x=6y-2

5x=6(1-x/3)-2
5x=(6-6x/3)-2
5x=2-2x-2
7x=0
x=0
y=1-(0)/3
y=1/3
-----------------------
the second one

x=-2y+18
5y=3x+1

5y=3(-2y+18)+1
5y=-6y+54+1
5y=-6y+55
11y=55
y=5
x=-2(5)+18
x=-10+18
x=8

Answer 2

1) y= 1-x/3

2) 5x-6y= -2

Substitute the result for y in equation 1 into equation 2

2) 5x - 6(1 - x/3) = -2
5x - 6 + 2x = -2
7x = 4
x = 4/7

1) y = 1 - (4/7)/3
y = 1 - 4/21
y = 21/21 - 4/21
y = 17/21

Check

5(4/7) - 6(17/21) = - 2
20/7 - 102/21 = -2
60/21 - 102/21 = -2
-42/21 = -2
-2 = -2

1) 3x-5y= -1

2) x+2y= 18
x = 18 - 2y

1) 3(18 - 2y) - 5y = -1
54 - 6y - 5y = -1
-11y = -55
y = 5

x = 18 - 2(5)
x = 18 - 10
x = 8

Check
3(8) - 5(5) = -1
24 - 25 = -1
-1 = -1

Answer 3

substitute in 1- x?3 into the secodn equation. So 5x-6(1-x/3)=-2. Then you solve. Then you plug in the x you found to the equation you just solved To get y. Do the same for the second one.

Answer 4

5x - 6(1 - x/3) = - 2
5x - 6 + 2x = - 2
7x = 4
x = 4 / 7

y = 1 - 4/21
y = 17/21

x = 4/7 , y = 17/21

3x - 5y = - 1
- 3x - 6y = - 54-------ADD
-11y = - 55
y = 5

x + 10 = 18
x = 8

x = 8 , y = 5

Answer 5

for 1st one, it would be 5X+ 6(1-X/3)=-2 then solve for x
then you can substitute x into the 1st equation and get the solution

for the 2nd, subtract 2y from 2nd equation then substitute -2y+18 into 1st equation.

you'll get 3(-2Y+18)-5Y=-1

solve for y then plug it into an equation to solve for x