Mathematics 2001 JAMB Past Questions - Question 10: solve the equations; m² + n² = 29, m +n = 7

Correct Answer

D

Explanation

To solve the system of equations:Equation 1: m² + n² = 29Equation 2: m + n = 7We can use substitution or elimination method to solve for the variables m and n. Let's use the elimination method:From Equation 2, we can express m in terms of n:m = 7 - nSubstituting this value of m into Equation 1:(7 - n)² + n² = 29Expanding and simplifying:49 - 14n + n² + n² = 292n² - 14n + 20 = 0Dividing the equation by 2 to simplify:n² - 7n + 10 = 0Factoring the quadratic equation:(n - 2)(n - 5) = 0Setting each factor equal to zero:n - 2 = 0 or n - 5 = 0Solving for n:n = 2 or n = 5Now, substitute these values of n back into Equation 2 to solve for m:For n = 2:m + 2 = 7m = 7 - 2m = 5For n = 5:m + 5 = 7m = 7 - 5m = 2Therefore, the solutions to the system of equations are:m = 5, n = 2m = 2, n = 5