System of Equations

[Guest]

Solve the system of equations:

(x + y) / 3 + (x + y) / 2 = 5 / 6 [1]

(x - y) / 4 + (x - y) / 3 = 7 / 12 [2]

My attempt:

For [1] : Multiply by 6 (lcm): 2x + 2y + 3x + 3y = 5 [3]

Combining terms: 5x + 5y = 5 [4]

5x + 5y = 5 [5]

Divide by 5 : x + y = 1 [6]

Replacing [6] in [1] : 1 / 3 + 1 /2 = 5 / 6 [7]

For [2] : Multiply by 12: 3x - 3y + 4x - 4y = 7 [8]

Combining: 7x - 7y = 7 [9]

Divide by 7: x - y = 1 [10]

Replacing [10] in [7] : 1/ 4 + 1/3 = 7 / 12 [11]

Where am I correct ?

[Guest]

When you get x + y = 1
then x = 1 - y

You can replace x in the second equation with 1 - y. You do not need to do anything regarding the first equation.

[Guest]

Ok, thanks again.

[Guest]

When you simplified [1] you got x + y = 1 [6]
When you simplified [2] you got x - y = 1 [10]

[6] and [10] now become the 2 equations to solve.

If you add the 2 equations... [6] plus [10] you get 2x = 2
So x = 1
and then substitute this in either [6] or [10]
you get for [6] ..... 1 + y = 1
So ......y = 0

Ans ...... x = 1 and y = 0

Check ans in equation [1] gives 1/3 + 1/2 = 5 /6 .....OK

[Guest]

Thanks.

[Guest]

When you simplified [1] you got x + y = 1 [6]
When you simplified [2] you got x - y = 1 [10]

[6] and [10] now become the 2 equations to solve...

Yeah that is write and the best solution.

[Guest]

Guest wrote "Yeah that is write and the best solution."

I presume you mean "Yeah that is right and the best solution."

In english "write" means to make a mark with a pen, pencil, typing etc, etc......"right" means it is correct or true etc........