Question

Hey guyzz!! Good Morning:-)
Solve the following pairs of equations by reducing them to a pair of linear equations.
a) 1/2x + 1/3y = 2
1/3x + 1/2y = 13/6
Plss answer it fastly!!

Answer 1

1/2x + 1/3y = 2

1/3x + 1/2y = 13/6

Fractions are really annoying, so I will multiple 6 to both sides for both equations

3x + 2y = 12

2x + 3y = 13

Now I will multiply 2 to both sides of the top equation and 3 to both sides of the bottom equation

6x + 4y = 24

6x + 9y = 39

Now I subtract the lower equation from the upper equation

4y - 9y = 24 - 39

-5y = -15

y = 3

Now I plug this into the original equation

1/2x + 1/3y = 2

1/2x + 1 = 2

1/2x = 1

x = 2

This is by no means the fastest way to solve the problem, but it is safer and it's less likely to make a mistake.

(also how is it morning for u?)