Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p - q

Explanation

\(\frac{1}{4}\)p + 3p = 10...(1)

2p - \(\frac{1}{3}\)q = 7...(2)

Multiply equation (2) by 3 to clear fraction

3 x 2p - 3 x \(\frac{1}{3}\)q = 3 x 7

6p - q = 21

6p - 21 = q....(3)

substituting 6p - 21 for q in (1)

\(\frac{1}{4}\)p + 3(6p - 21) = 10...(4)

Multiply equation (4) by 4 to clear fraction

4 x \(\frac{1}{4}\)p + 4 x 3(6p - 21) = 4 x 10

p + 12(6p - 21) = 40

p + 72p - 252

73p = 292

p = \(\frac{292}{73}\)

= 4