Question

Solve each of the following systems of equations by the method of cross-multiplication:
mx-ny=m²+n²x+y=2m

Answer 1

answer : x = (m + n) and y = (m - n)

given equations ,

mx - ny = m² + n² ⇒mx + (-n)y + {-(m² + n²)} = 0

x + y = 2m ⇒x + y + (-2m) = 0

by cross multiplication method,

x/{(-n) × (-2m) - 1 × -(m² + n²)} = -y/{m × (-2m) - 1 × -(m² + n²)} = 1/{m × 1 - (-n) × 1}

⇒x/{2mn + m² + n²} = -y/{-2m² + m² + n²} = 1/(m + n)

⇒x/(m + n)² = y/(m² - n²) = 1/(m + n)

⇒x/(m + n)² = y/(m + n)(m -n) = 1/(m + n)

x = (m + n)²/(m + n) = (m + n)

y = (m + n)(m - n)/(m + n) = (m - n)

hence x = m + n and y = m - n

Answer 2

Answer:

Thanx for 13 and a few more years of