Can you help me with the substitution method?

Question

1. x + 3y = 23 3x - 2y = 3
Solve and check using the substitution method.

Answer 1

x + 3y = 23
3x - 2y = 3

Start by solving one of the equations for a single variable. For example solve the first equation for x:
x + 3y = 23
x = 23 - 3y

Now substitute this into the second equation:
3x - 2y = 3
3(23 - 3y) - 2y = 3

Distibute the 3 through the parentheses:
69 - 9y - 2y = 3

Simplify:
69 - 11y = 3

Subtract 3 from both sides:
66 - 11y = 0

Add 11y to both sides:
66 = 11y

Divide both sides by 11:
y = 66/11
y = 6

Now plug this back into any equation to solve for x:
x + 3y = 23
x + 3(6) = 23
x + 18 = 23
x = 23 - 18
x = 5

So the answer is x = 5, y = 6

Double-check to confirm.

Answer 2

solve x+3y=23 for x

get x=23-3y

substitute 23-3y in for x in second equation
3(23-3y)-2y=3
69-9y-2y=3
69-11y=3
-11y=3-66
-11y=-66
y=6

Now substitute 6 for y in first equation
x+3y=23
x+3(6)=23
x+18=23
x=23-18
x=5

Answer 3

x+3y=23 --> x=23-3y
Replace to 3x - 2y =3
--> 3(23-3y)-2y=3-->11y=66 -->y=6
x=23-3y=5

Answer 4

x+3y=23 =>x=23-3y
3x-2y=3=>3(23-3y)-2y=3

69-11y-3=0
66=11y => y=6

x=23-3(6)=23-18=5

x=5 and y=6

Answer 5

x + 3y = 23 ...................i
3x - 2y = 3 ....................ii
from i x = 23 - 3y .........iii
put iii in ii
3 (23 - 3y) - 2y = 3
69 - 9y - 2y = 3
-11y = 3 - 69
-11y = - 66
y = 6
put y = 6 in iii
x = 23 - 3*6
x = 23 - 18
x = 5
so x = 5 , y = 6.
check: x + 3y = 23
5 + 3*6 = 5 + 18 = 23.

Answer 6

x+3y=23
x=23-3y subst into the other eq.
3(23-3y)-2y=3
69-9y-2y=3
-11y=-66
y=6
x=23-3(6)
x=5

Answer 7

x+3y=23
x=23-3y

3x-2y=3
3*(23-3y)-2y=3
69-9y-2y=3
69-11y=3
-11y=-66
y=6
x=23-3y=23-3*6=23-18=5
y=6 x=5

Now check
x+3y=5+6*3=5+18=23, it checks