Find the value of p if $\frac{1}{4}$p + 3q = 10 and 2p - $\frac{1}{3}$q = 7

Analyze the question: We have two simultaneous linear equations in p and q, and we need p.

(1) p/4 + 3q = 10 (2) 2p − q/3 = 7

Clear the fractions: (1) × 4: p + 12q = 40 (2) × 3: 6p − q = 21

Solve by elimination: From the second equation, q = 6p − 21.

Substitute into p + 12q = 40: p + 12(6p − 21) = 40 p + 72p − 252 = 40 73p = 292 p = 4

Check: q = 6(4) − 21 = 3.

• Equation 1: 4/4 + 3(3) = 1 + 9 = 10 ✓
• Equation 2: 2(4) − 3/3 = 8 − 1 = 7 ✓

Tip: When simultaneous equations contain fractions, multiply each equation by its denominator first to get whole-number coefficients. Then use substitution or elimination. Always check your answer in both original equations, because it takes only a few seconds and catches mistakes.