if 3p+q=16 and 8p-3q=20, what is the value of 5p-4q

Question

is this possible to solve knowing those two things?

Answer 1

3p + q = 16        eq1

8p - 3q = 20        eq2

 

We have here a system of equations.  We will work with these two equations to find the value of p and q.  Then use p and q to evaluate the expression.

 

First, we can substitute eq1 into eq2.  This will give us an equation with only one variable.

 

8p - 3(16 - 3p) = 20

 

8p - 48 + 9p = 20

 

17p = 68

    p = 4

 

Substitute this value of p into eq1 to solve for q.

 

q = 16 - 3p

q = 16 - 3(4)

q = 16 - 12

q = 4

 

p = 4 = q

 

Use these values to evaluate the expression.

 

5p - 4q =

5(4) - 4(4) =

20 - 16 =

4