HI STEVE,

THANKS for your reply back it was the wrong answer the one you worked, yes a hard question,
here is an example of simultaneous questions.

x-2/3 + y-1/4 =13/12 (1)

2-x/2 + 3+y/3 =11/6 (2)

first step is to get rid of fractions.
in equation (1) the lcm of denominators is 12 .multiply each term by 12,

4(x-)+3(y-1) = 13
4x-8+3y-3= 13
4x+3y = 24 (3)
in equation (2) the lcm of denominator is 6.
multiply each term by 6,
3(2-x)+2(3+y)=11
6-3x+6+2y= 11
-3x+2y=-1 (4)
to eliminate y we multiply equation (3) by 2 and equation 940 by 3.
8x+6y=48(5)
-9x=6y=-3(6)
subtracting equation (6)from equation (5),
(8x-(-9x)+(6y-6y)= (48-(-3)
17x= 51
x= 3
try the previous question again please
thanks

I think you are referring to this earlier post by you

http://www.jiskha.com/display.cgi?id=1415787409

I agree with Steve's answer, I subbed his answer back in the original equation, and it worked.
Steve's solution was correct, perhaps you typed it incorrectly.

As to this new question ....
You MUST put in brackets so the question can be properly interpreted, (as Steve did for you)

You seem to be working it out as if brackets had been there but they must be there.

To solve the system of equations, we can use the method of elimination. Here are the steps:

1. Write down the two equations:
4x + 3y = 24 (3)
-3x + 2y = -1 (4)

2. Multiply equation (3) by 3 and equation (4) by 2 to eliminate the y term. This gives us:
12x + 9y = 72 (5)
-6x + 4y = -2 (6)

3. Now, subtract equation (6) from equation (5):
(12x - (-6x)) + (9y - 4y) = (72 - (-2))
18x + 5y = 74

4. Simplify the equation obtained:
18x + 5y = 74 (7)

5. Now solve equations (7) and (4) simultaneously. Multiply equation (4) by 9 to eliminate the x term:
9(-3x + 2y) = 9(-1)
-27x + 18y = -9 (8)

6. Add equations (7) and (8):
(18x - 27x) + (5y + 18y) = (74 - 9)
-9x + 23y = 65

7. Now, solve equation (9) and equation (6) simultaneously. Multiply equation (6) by 9 to eliminate the x term:
9(-6x + 4y) = 9(-2)
-54x + 36y = -18 (10)

8. Add equations (9) and (10):
(-9x - 54x) + (23y + 36y) = (65 - 18)
-63x + 59y = 47

9. Now we have a new equation (-63x + 59y = 47). To solve for x, substitute the value of y obtained from equation (8):
-63x + 59(2x - 1) = 47
-63x + 118x - 59 = 47
55x = 106
x = 106/55
x ≈ 1.927

10. Finally, substitute the value of x into one of the original equations (3 or 4) to solve for y. Let's use equation (3):
4(1.927) + 3y = 24
7.708 + 3y = 24
3y = 24 - 7.708
3y ≈ 16.292
y ≈ 16.292/3
y ≈ 5.431

So, the solution to the system of equations is approximately (x, y) ≈ (1.927, 5.431).

To solve the given simultaneous equations:

Equation (1): $\frac{x-2}{3} + \frac{y-1}{4} = \frac{13}{12}$ (1)
Equation (2): $\frac{2-x}{2} + \frac{3+y}{3} = \frac{11}{6}$ (2)

First, we need to eliminate the fractions. To do this:

For equation (1), the least common multiple (LCM) of the denominators 3 and 4 is 12. So, we can multiply each term in equation (1) by 12 to get rid of the fractions:

$4(x-2) + 3(y-1) = 13$

Simplifying equation (1) gives us:
$4x - 8 + 3y - 3 = 13$
$4x + 3y = 24$ (3)

For equation (2), the LCM of the denominators 2 and 3 is 6. So, we can multiply each term in equation (2) by 6:

$3(2-x) + 2(3+y) = 11$

Simplifying equation (2) gives us:
$6 - 3x + 6 + 2y = 11$
$-3x + 2y = -1$ (4)

Now, we have a system of two linear equations:
Equation (3): $4x + 3y = 24$
Equation (4): $-3x + 2y = -1$

To eliminate y, we can multiply equation (3) by 2 and equation (4) by 3:

$8x + 6y = 48$ (5)
$-9x + 6y = -3$ (6)

Now, we can subtract equation (6) from equation (5):

$(8x - (-9x)) + (6y - 6y) = (48 - (-3))$

Simplifying this equation gives us:
$17x = 51$
$x = 3$

Now that we have the value of x, we can substitute it back into either equation (3) or (4) to find the value of y. Let's use equation (3):

$4(3) + 3y = 24$

Simplifying this equation gives us:
$12 + 3y = 24$
$3y = 24 - 12$
$3y = 12$
$y = 4$

Therefore, the solution to the given simultaneous equations is:
$x = 3$
$y = 4$

Please let me know if there is anything else I can assist you with.