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Question
Solve the following simultaneous liner equations by subsitution method
mx-ny=m²+n²
x+y=2m
Solve the following simultaneous liner equations by subsitution method
mx-ny=m²+n²
x+y=2m
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Solution
mx - ny = m2 + n2
⇒ mx - ny = m2 + n2 +2mn - 2mn
⇒ mx - ny = (m + n)2 - 2mn [identity a2 + 2ab +b2 = (a+b)2] → 1
x + y = 2m → 2
Substituting eq. 2 in eq. 1.
mx - ny = (m + n)2 - (x + y)n
mx - ny = (m + n)2 - nx - ny
Addding ny to both sides, you get:
mx = (m + n)2 - nx
mx + nx = (m + n)2
x(m + n) = (m + n)2
Dividing both sides by (m + n), you get:
x = m + n
Substituting x = m + 2 in eq. 1.
(m + n) + y = 2m
y = 2m - m - n
y = m - n
Therefore, x = m + 2, y = m - n
hope it helps
mx - ny = m2 + n2
⇒ mx - ny = m2 + n2 +2mn - 2mn
⇒ mx - ny = (m + n)2 - 2mn [identity a2 + 2ab +b2 = (a+b)2] → 1
x + y = 2m → 2
Substituting eq. 2 in eq. 1.
mx - ny = (m + n)2 - (x + y)n
mx - ny = (m + n)2 - nx - ny
Addding ny to both sides, you get:
mx = (m + n)2 - nx
mx + nx = (m + n)2
x(m + n) = (m + n)2
Dividing both sides by (m + n), you get:
x = m + n
Substituting x = m + 2 in eq. 1.
(m + n) + y = 2m
y = 2m - m - n
y = m - n
Therefore, x = m + 2, y = m - n
hope it helps
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