Mathematics 2023 JAMB Past Questions - Question 6: Solve the equations: P2+q2=29, P+q = 7

Correct Answer

C

Explanation

To solve the system of equations P2+q2=29 and P+q=7 Here's how you can solve it using substitution:From the second equation, solve for one variable in terms of the other. Let's solve for P in terms of  q: P=7−q Now substitute this expression for P into the first equation: (7−q)2+q2=29 Expand and solve for q: 49−14q+q2+q2=29 2q2−14q+20=0 (q−5)(q−2)=0So, q=5 or q=2. Divide through by 2: q2−7q+10=0This quadratic equation can be factored: Now, substitute each value of q back into the equation P=7−q to find the corresponding values of P: When q=5, P=7−5=2When q=2, P=7−2=5 Therefore, the solutions to the system of equations are P=2,q=5 and P=5,q=2.