## Solve the equation: m² + n² = 29, m + n = 7

**A.** (5, 3) and (3, 5)

**B.** (2, 5) and (5, 2)

** C.** (5, 2) and (5, 3)

**D.** (2, 3) and (3, 5)

**QUICK ANSWER…**

**B**

**DETAILS…**

**You should save time and quickly realize that option B is the most reasonable, this is because m + n = 7, and only option B completely satisfy this.**

**Besides, this is a quadratic simultaneous equation, we’re going to be solving it by substitution method…**

**m****²**** + n****²**** = 29 …………………..eq 1**

**m + n = 7 ……………………….eq 2**

**from eq 2,**

**m = 7 – n**

**substituting m for ‘7 – n’ in eq 1, we have:**

**(7 – n)****²**** + n****²**** = 29**

**(7 – n)(7 – n) + n****²**** = 29**

**49 – 7n – 7n + n****² + n²**** = 29**

**49 – 14n + 2n****²**** = 29**

**Rearranging;**

**2n****²**** – 14n + 49 – 29 = 0**

**2n****²**** – 14n + 20 = 0**

**Dividing through by 2, we have:**

**n****²**** – 7n + 10 = 0**

**factorizing this, we have:**

**n****²**** – 5n – 2n + 10 = 0**

**n(n – 5) – 2(n – 5) = 0**

**(n – 5)(n – 2) = 0**

**(n – 5) = 0, n = 5**

**(n – 2) = 0, n = 2**

**n = 5 or 2**

**to solve for m, recall that m + n = 7,**

**m = 7 – n**

**when n = 5, m = 7 – 5 = 2**

**and when n = 2, m = 7 – 2 = 5**

**hence, we have the answer, option B.**

**Now for the right answer to the above question:**

**Option A is incorrect. 5 + 3 is not = 7****Option B is correct. 5 + 2 = 7****C is incorrect. 5 + 3 is not = 7****D is not the correct answer. 2 + 3 is not = 7**

**KEY-POINTS…**

**You may please note these/this:**

**Under exam conditions (multiple choice), there will be no need to solve this in detail, just inspect the options and realize that only option B reasonably satisfies one of the equations.****If you love our answers, you can login to comment and say hi to us at the comment section…**

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**/ culled from 2020 JAMB-UTME mathematics past question 11 /**