Hence we get p=1/x and q=1/y. So we can change the question ;

6p – 7q = 8 ;

15p – 14q = 21.

You can solve this question easily multiplying by 2 the first equation (6p – 7q = 8 ), so it change to 12p – 14q = 16.

You can solve this with elimination, to get p=5/3 and q=2/7. Don’t forget to convert p=1/x so x=1/p and q=1/y to y=1/q. The real answer was x= 3/5=0.6 and y= 7/2=3.5

About g(f(x)), this is a real classic problem for me. Many student confused with the parenttheis. You can assume “ f(x) as x for the g ”.

Example: if you have function f(x) = 2x + 3 and you have determined the value of x =4, then you have f(x) = f(4) = 2(4) + 3 = 8 + 3 = 11. So, every CHARACTER in the bracket, is multiplied by 2, then added by 3.

In other word ; g(f(x)) are function which are the independent variables (usually just “x” in “simple” function) are depending on the value of f(x).

I really hope this can help you. Feel free to contact me if you have any difficulty in any subject of math, physic, and chemistry. You can contact me by email. Cheers!!!

15/x-14/y=21 —-(2)

From (1),

6/x=8+7/y

1/x=1/6(8+7/y) —-(3)

Subst (3) into (2)

15/6(8+7/y)-14/y=21

20+35/2y-14/y=21

Multiplying throughout by y you get…

20y+35/2-14=21y

7/2=y

Subst y=7/2 into (1)

6/x-7/(7/2)=8

6/x-2=8

6/x=10

6=10x

x=3/5

So x=3/5 and y=7/2

As for g(f(x)), you need to know what f(x) and g(x) is.

eg f(x)=x+1 and g(x)=x-1

Subst f(x) in g(f(x)) first to get g(x+1)

Then you solve for g(x+1) which will give you (x+1)-1.

Simplifying you get x.

Hope that helps

If not, solve both equations for x (i.e. x=something*y+whatever) and set them equal to each other, then solve for y. Take your number for y, and plug it into one of the equations to solve for x.