one one half of x minus two thirds of y equals three. Solve for both x and y.?

Question

I've been dwelling on this one for a while and just can't seem to figure it out. Please help! Thanks!

I think that the answers are x= 1.5 and y= 0...that just doesn't seem right though. Please explain how you did your steps. Thanks!

Answer 1

Is it
(1 1/2)x - (2/3)y = 3
or
(1/2)x - (2/3)y = 3

Anyway... You can solve for one variable in terms of the other, but you can't find the solution for x and y because you only have one equation. (You need two equations to solve for 2 variables.)

(1 1/2)x - (2/3)y = 3
(3/2)x - (2/3)y = 3
(multiply everything by 6 to get rid of fractions)
9x - 4y = 18
9x = 4y + 18
x = (4/9)y + 2

and...
9x - 4y = 18
-4y = 18 - 9x
4y = 9x - 18
y = (9/4)x - (9/2)

If it's this equation:
(1/2)x - (2/3)y = 3
(multiply everything by 6)
3x - 4y = 18
3x = 4y + 18
x = (4/3)y + 6

and...
3x - 4y = 18
-4y = -3x + 18
4y = 3x - 18
y = (3/4)x - (9/2)

Answer 2

22 and 12

Answer 3

You can solve for x or y but the answer will be in term of the other variable.
If you want to find the real number for x and y, you need another equation that comes with x and y also.
To solve the equations with 2 unknown (x, y), you need 2 equations.

Answer 4

Convert the fraction to standard form

1/2x - 2/3y = 3

Multiply both sides of the equation by 6

6(1/2x) - 6(2/3y = 6(3)

3x - 2y = 18

- - - - - - - - - --

y intercept

x = 0

3x - 2y = 18

3(0) - 2y = 18

0 - 2y = 18

- 2y = 18

- 2y / - 2 = 18 / - 2

y = 18 / - 2

y = - 9

- - - - - - - - - - --

x intercept

y = 0

3x - 2y = 18

3x - 2(0) = 18

3x - 0 = 18

3x / 3 = 18 / 3

x = 18 / 3

x = 6

- - - - - - - - - -

convert 3x - 2y = 18 to Slope intercept form

y = mx + b

3x - 2y = 18

3x - 2y - 3x = - 3x + 18

- 2y = - 3x + 18

- 2y / - 2 = - 3x / 2 + (18 / - 2)

y = - 3x / 2 + (- 9)

y = 3/2x - 9

- - - - - - -

Slope = 3/2

y intercept = - 9

- - - - - - - - -s-

Answer 5

you need two equations to figure this out