finding p and q?

Question

I've managed other problems like this, but this one has me completely stumped.

Solve the following equations. Find the appropriate values for p and q.

3p - 2q = 37
p + 4q = 3

the values of p and q are the same for each equation, but I can't make it fit.

Answer 1

[Equation 1] 3p - 2q = 37
[Equation 2] p + 4q = 3

Add 2*[Equation 1] + [Equation 2] to get
7p = 77
==> p = 11

Plug p=11 in for [Equation 2] and solve for q
11 + 4q = 3
==> 4q = -8
==> q = -2

Answer 2

These are simultaneous equations in 2 unknowns.
Equation 1: 3p - 2q = 37
Equation 2: p + 4q = 3
Multiply equation 1 by 2
6p - 4q = 74
Add to equation 2
7p = 77
p = 11
Substitute in equation 2
11 + 4q = 3
Subract 11 from both sides
4q = -8
q = -2
Substitute in equation 1
33 - (-4) = 37
Proof left = right side

Answer 3

the second equations says p + 4q = 3
so p = 3 - 4q

Now you replace p by 3 - 4q in the first equation (as they are the same)

you get:
3*(3-4q) - 2q = 37
9 - 12 q - 2q = 37
9 - 14q = 37
-14q = 28
q = -2

finally: p = 3 - 4q = 3 - 4*(-2) = 3 + 8 = 11

So p = 11 and q =-2.

Proof:
3*11 - 2*(-2) = 33 + 4 = 37 OK
11 + 4*(-2) = 11 - 8 = 3 OK

Answer 4

multiply the first equation by 2 to give 6p - 4q = 74

6p - 4q = 74
p + 4q = 3
add the equations

= 7p + 0 = 77
p = 77/7
p = 11

p + 4q =3
11 + 4q =3
4q = 3-11
q = -8/4
q= -2

Answer 5

p=11
q= -2
i used substitution
p+4q=3
p= -4q + 3
3(-4q+3) -2q=37 subsititute
-12q + 9 - 2q= 37
-14q+ 9= 37 combine like terms
-14q = 28
q = -2

and then subsititute that into the other equation

Answer 6

3p - 2q = 37
p + 4q = 3

p = 3 - 4q
3p - 2q = 37
3 (3 - 4q) - 2q = 37
9 - 12q - 2q = 37
-14q = 37 - 9
-14q = 28
q = -2

p = 3 - 4q
p = 3 - 4(-2)
p = 3 + 8
p = 11

Answer 7

3p - 2q = 37, so

6p - 4q = 74
p + 4q = 3
------------------
7p .... = 77
p = 11

11 + 4q = 3
4q = -8
q = -2