solve this in 3 variables..
i don't know where to start,,:((
y/4+z/3-x/2=4
y/2-x/6+z/15=2
y/8+z/5-x/3=2
first find the LCD then solve as you would simultaneous equations in three unknowns
try it and post back if you need more help
To solve this system of equations with three variables, we can use the method of elimination or substitution. Let's use the method of elimination in this case.
The given system of equations is:
1) y/4 + z/3 - x/2 = 4
2) y/2 - x/6 + z/15 = 2
3) y/8 + z/5 - x/3 = 2
Step 1: Eliminate the x-terms by multiplying each equation by the appropriate coefficients:
Multiply equation 1 by 6, equation 2 by 2, and equation 3 by 3 to eliminate the x-terms.
Equation 1: 6(y/4 + z/3 - x/2) = 6(4) => 3y/2 + 2z - 3x = 24
Equation 2: 2(y/2 - x/6 + z/15) = 2(2) => y - x/3 + z/8 = 4
Equation 3: 3(y/8 + z/5 - x/3) = 3(2) => 3y/8 + 3z/5 - x = 6
Step 2: Now we have a new system of equations:
4) 3y/2 + 2z - 3x = 24
5) y - x/3 + z/8 = 4
6) 3y/8 + 3z/5 - x = 6
Step 3: Eliminate the y-term by multiplying equation 5 by 3 and subtracting equation 6 from it:
Multiply equation 5 by 3: 3(y - x/3 + z/8) = 3(4) => 3y - x + 3z/8 = 12
Subtract equation 6 from the modified equation 5: (3y - x + 3z/8) - (3y/8 + 3z/5 - x) = 12 - 6
Simplifying, we get: (3y - 3y/8) + (x + x/8) + (3z/8 + 3z/5) = 6
Combining like terms, we have: 23x/8 + 39z/40 = 6
Step 4: Solve the resulting equation for x:
Multiply through by the least common multiple of the denominators (8 * 40 = 320):
320 * (23x/8 + 39z/40) = 320 * 6
This simplifies to: 920x + 312z = 1920
Step 5: Simplify other two equations:
Transform equation 4 and 6 into simple fractions:
4) 3y/2 + 2z - 3x = 24 => 6y + 8z - 12x = 96 (Multiply through by 2)
6) 3y/8 + 3z/5 - x = 6 => 15y + 24z - 40x = 120 (Multiply through by 40)
Now we have the following three equations:
7) 920x + 312z = 1920
8) 6y + 8z - 12x = 96
9) 15y + 24z - 40x = 120
Step 6: Solve the system of equations 7, 8, and 9 using any method such as substitution or elimination to find the values of x, y, and z.
Alternatively, you can use online calculators or software to solve systems of equations to find the numerical values of x, y, and z.