How can you solve the set of 4-(y-3)=x+3 and 10/3+x/3=2+(y+12) using any convenient/applicable method?

Question

need help

thanks for the answers... ive compared these answers to my answers on all my trials but unfortunately i got it all wrong... anyway, thanks, ill analyze your answers and see what part ive done wrong

Answer 1

I figure you are talking about a system of equations:

4 - (y-3) = x + 3
4 - y + 3 = x + 3
4 - y = x

10/3 + x/3 = 2 + (y + 12)
10 + x = 6 + 3y + 36
10 + x = 3y + 42
x = 3y + 32

From this, you can use substitution method:
4 - y = 3y + 32
4 = 4y + 32
-28 = 4y
y = -7

Then substitute that value of y to any of the equations:
4 - y = x
4 - (-7) = x
4 + 7 = x
x = 11

The solution set is {(11, -7)}

Answer 2

4-(y-3)=x+3
---> 4 - y + 3 = x + 3
---> x = 4 - y ---> Equation (1)

10/3+x/3=2+(y+12)
---> (10 + x)/3 = 2 + y +12
---> 10 + x = 3(y + 14) ---> Equation (2)

Subsitute Equation (1) into (2),
10 + (4 - y) = 3y + 42
3y - y = 14 - 42
2y = -28
y = -28/2 = -14

Substitute the value of y into Equation (1),
x = 4 - (-14) = 4 + 14 = 18

Answer 3

4-(y-3) = x + 3
// distribute the negative sign
4-y+3 = x+3
x = 4-y

10/3 + x/3 = 2 + (y+12)
// combine 10/3 + x/3 and replace x with 4-y
(10 + 4 - y)/3 = 2 + (y + 12)
// simplify the right side
(10 + 4 - y)/3 = 14 + y
// multiply both sides of the equation by 3
10 + 4 - y = 42 + 3y
// combine like terms
4y = -28
// divide both sides of the equation by 4
y = -7

x = 4-y
x = 11

Answer 4

I had already solved it in answer to your previous question. Similarly you should have solved this also. It shows that you are not interested in learning rather you just want to copy the solution. Any way, I am solving it again

First equation
4-(y-3)=x+3
4-y+3=x+3
x=-y
put this value of x in second equation
10/3+(-y)/3=2+(y+12)
(10-y)/3=y+14
10-y=3(y+14)
10-y=3y+42
4y=-32
y= -8
since x=-y
x=-(-8)
x=8

Answer 5

4 - y + 3 = x + 3
x + y = 4

10 + x = 6 + 3y + 36

x - 3y = 32
- x - y = - 4-----ADD
- 4y = 28
y = - 7

x + 21 = 32
x = 11
SOLUTION is x = 11 , y = - 7

Answer 6

4-y+3=x+3
x=4-y -----------------(1)
(10+x)/3=y+14
10+x=3y+42
x=3y+32 ------------------(2)

=) 4-y=3y+32
-4y=28
y= (-7)
putting y= -7 in eq(1)

=) x= 11