Question

First clear the system of fractions, then solve by substitution.
x/2-y/3=5/6
x/5-y/4=29/10

Answer 1

To get rid of fractions, you need to multiply each equation by its LCD. The lcd of the first one would be 12, the lcd of the second one would be 20.

x/2-y/3=5/6 <-------*12
x/5-y/4=29/10 <-------*20
----------------------------
6x-4y=10
4x-5y=58

Solve for y in one of them:
6x-4y=10
-4y=-6x+10
y=3/2x-5/2

Substitute that into the other equation and solve for x.

4x-5(3/2x-5/2)=58

4x-15/2x+25/2=58
4x+5x=58
9x=58
x=58/3


Substitute the value of x into one of the equations and solve for y.

6(58/3)-4y=10
116-4y=10
-4y=-106
y=53/2


Check yourself by plugging both x and y into the equation and see if its true.

6(58/3)-4(53/2)=10
116-106=10
10=10

That's true. So x=58/3 and y=53/2

Answer 2

LCD 2,3,6 = 6