If 5y = 6x +16 and 9x= 7y - 20, what is the value of 3x - 2y?

Answer 1

Liz, both Paul and Aaron have shown how to do this in general. I think there’s a shortcut in this particular case.

If 5y = 6x +16 and 9x= 7y - 20, what is the value of 3x - 2y?

Transform 9x = 7y -20 to

9x -7y = -20

Transform 5y = 6x + 16 to

6x - 5y = -16

Now subtract the second one from the first

3x - 2y = -4

You don’t usually get such a benevolent problem!

Answer 2

If 5y = 6x +16 and 9x= 7y - 20, what is the value of 3x - 2y?

I'm going to try to work with this as written. We first want to isolate the X in the first equation by subtracting 16 from both sides.

5y-16=6x then to get the variable by itself, divide all by 6 so x=(5y-16)/6

Next the same with the second for Y. 9x+20=7y, then y=(9x+20)/7. From here it's a matter of putting these values into 3x-2y which will involve lots of nasty fractions. Good luck.

Answer 3

Just solve the simultaneous set for x and y as follows

Multiply the first equation by 3 and the 2nd equation by 2.

Add the 2 equations to get y=8.

Plug y=8 into the first equation to get x=4.

Check your result in the second equation.

Then compute the required value.