Three times one number is twice the second number. twice the first number is 3 more than the second number. what are the numbers?

Ok so lets say the first number is x and the second number is y we will use a system of equations to solve.

"Three times one number is twice the second" this equation is 3x=2y

" Twice the first number is 3 more than the second number." this equation would be 2x=y+3

To solve for x, change the second equation to y = 2x-3 by simply subtracting 3 from y to get y by itself.

Plug 2x-3 in for y in the first equation

3x=2 (2x-3) solve for x - distribute the 2

3x=4x-6 subtract the 4x from both sides

-x = - 6 divide both sides by - 1 to get rid of the - x

x=6 now plug this into x in any of the 2 equations and you will find y

2x=y+3

2 (6) = y+3

12=y+3

9=y

first number is 6 second number is 9

Let x be the 1st number & y the 2nd

3x=2y (1st equation)

and

2x=y+3 (2nd equation) = = = > 2x-3 = y (3rd equation) & y=9

Substitute in 1st equation, y but its value in the 3rd

===>3x = 2 (3x-3) = = = >solve for x=6