Solve the simultaneous equations
3/x+5/y=4 and 9/x+4/y=5
3/x + 5/y = 4
9/x + 4/y = 5
subtract the bottom from 3 times the top
11/y = 7
y = 11/7
so x = 11/3
Looks like this one is too hard for the bot to handle, so ....
I would multiply the first by 3 to get
9/x + 15/y = 12
subtract the 2nd from this:
0 + 11/y = 7
7y = 11
y = 11/7
sub into the first:
3/x + 5/(11/7) = 4
3/x + 35/11 = 4
3/x = 9/11
9x =33
x = 11/3
sorry oobleck for the duplicate solution,
but at least we are correct
To solve the simultaneous equations:
1. Start by rearranging the equations to isolate one variable on one side of the equation in terms of the other variable.
For the first equation, multiply both sides by xy to remove the denominators:
3y + 5x = 4xy
For the second equation, similarly multiply both sides by xy:
9y + 4x = 5xy
2. Now you have two equations with two variables. You can solve this system of linear equations using various methods, such as substitution or elimination.
Let's use the elimination method:
Multiply the first equation by 4 and the second equation by 5. This way, the coefficients of 'x' will be equal in both equations:
12y + 20x = 16xy
45y + 20x = 25xy
3. Subtract the first equation from the second equation:
(45y + 20x) - (12y + 20x) = 25xy - 16xy
33y = 9xy
Divide by 9y:
33/9 = x
x = 11/3
4. Substitute the value of x back into one of the original equations and solve for y:
3/(11/3) + 5/y = 4
3 * 3/11 + 5/y = 4
9/11 + 5/y = 4
Subtract 9/11 from both sides:
5/y = 4 - 9/11
5/y = 44/11 - 9/11
5/y = 35/11
Cross-multiply:
5 * 11 = 35 * y
55 = 35y
Divide by 35:
y = 55/35
y = 11/7
The solution to the simultaneous equations is x = 11/3 and y = 11/7.