Help with the substitution method?

First, choose a variable to substitute. Let's be random and pick "q."

Next, choose one of the equations to solve for "q." Again, let's be random and pick the second equation.

Solving for q, we get:

5p+7q=1 (subtract 5p)
7q=1-5p (divide by 7)
q = (1-5p)/7

Next, you have to take the equation that you just found and plug it back into the other (first) equation, and solve for p.

4p-2q=16 (plug in equation)
4p-2[(1-5p)/7]=16 (subtract 4p)
-2[(1-5p)/7]=16-4p (divide by -2 to cancel out the numerator on the left, and distribute on the right)
(1-5p)/7 = -8+2p (multiply by 7 to cancel on denominator on the left, and distribute on the right)
1-5p= -56+14p (rearrange terms to combine similar ones)
57=19p (divide by 19 to solve for p)
p=3

Now that you have p, you can plug it back into either one of the two ORIGINAL equations and solve for q. Let's plug it into the first.

4p-2q=16 (plug in 3 for p)
4(3)-2q=16 (distribute)
12-2q=16 (subtract 12 from both sides)
-2q=4 (divide by -2)
q=-2

If you want, you can plug each answer into both equations and make sure they add up correctly.

Hope this helps. :)

4p = 16 + 2q
p = 4 + q/2

20 + 5q/2 + 7q = 1
19q/2 = - 19
q/2 = - 1
q = - 2

4p + 4 = 16
p = 3

p = 3 , q = - 2

4p - 2q = 16
5p + 7q = 1

4p - 2q = 16
2p - q = 8
q = 2p - 8

5p + 7q = 1
5p + 7(2p - 8) = 1
5p + 14p - 56 = 1
19p = 1 + 56
19p = 57
p = 57/19
p = 3

4p - 2q = 16
2(3) - q = 8
q = 6 - 8
q = -2

∴ p = 3 , q = -2

Focus on one problem

4p-2q=16

let's go for q on this one...

-2q= -4p+16

divide by -2

q=2p-8

now we sub in q in the other problem

5p+7(2p-8)=1
5p+14p-56=1

combine like terms

19p=57
p=3

now solve for q

4(3)-2q=16
12-2q=16
-2q=4
q=-2

final answer

p=3 and q=-2

(i) 4p − 2q = 16 ⇒ 2p − q = 8
(ii) 5p + 7q = 1

(i) ⇒ 2p = 8 + q
⇒ 2p − 8 = q

Substitute this value for q into equation (ii):
⇒ 5p + 7(2p − 8) = 1
⇒ 5p + 14p − 56 = 1
⇒ 19p = 57
⇒ p = 57 ÷ 19
⇒ p = 3

Substitute this value of p into equation (i):
⇒ 2(3) − q = 8
⇒ 6 − q = 8
⇒ 6 = 8 + q
⇒ q = −2

Check:
5p + 7q = 1
⇒ 5(3) + 7(−2) = 1
⇒ 15 − 14 = 1
⇒ 1 = 1 ✓


p is equal to 3, q is equal to −2.

solve first one for q

-2q = 16 -4p

q = -8 + 2p

substitue

5p + 7 ( -8 + 2p ) = 1

5p - 56 + 14p = 1

19p = 57

p = 3

4(3) - 2q = 16

12 - 2q = 16

-2q = 4

q = -2