peanuts worth $2.25 a pound were mixed with 14 pounds of cashews worth $3.25a pound to produce a mixture worth $2.65 a pound. how many pounds of peanuts were

Sorry....I don't see this as a substitution or elimination problem......here's how I would solve it......

Let x be the lbs. of peanuts used....and we have

2.25x + 3.25 (14) =  2.65(14 + x)    simplify

2.25x + 45.50   = 37.10 + 2.65x       subtract 2.25x, 37.10 from both sides

8.40  = .40x      divide both sides by .40

21  = x   = 21 lbs. of peanuts

[Maybe someone else on here knows a different method]

Let p=lb of peanuts        [HERE IS A METOD OF SUBSTITUTION AND ELIMINATION]

Let m=lb of mixed nuts

p+14=m

2.25p + 45.5=2.65m

Solve the following system:
{p+14 = m}
2.25 p+45.5 = 2.65 m

In the first equation, look to solve for m:
{p+14 = m
2.25 p+45.5 = 2.65 m

p+14 = m is equivalent to m = p+14:
{m = p+14
2.25 p+45.5 = 2.65 m

Substitute m = p+14 into the second equation:
{m = p+14
2.25 p+45.5 = 2.65 (p+14)

2.65 (p+14) = +(2.65 p+37.1) = 2.65 p+37.1:
{m = p+14
2.25 p+45.5 = 2.65 p+37.1

In the second equation, look to solve for p:
{m = p+14
2.25 p+45.5 = 2.65 p+37.1

2.25 p+45.5 = (9 p)/4+91/2 and 2.65 p+37.1 = (53 p)/20+371/10:
(9 p)/4+91/2 = (53 p)/20+371/10

Subtract (53 p)/20+91/2 from both sides:
{m = p+14
-(2 p)/5 = -42/5

Multiply both sides by -5/2:
{m = p+14
p = 21

Substitute p = 21 into the first equation:
Answer: | 
| {m = 35 Pounds of mixed nuts.
    p = 21 Pounds of peanuts.