Solve the following system of simultaneous linear equations by the substitution method:
mx - ny = m² + n²
x + y = 2m

Question

Solve the following system of simultaneous linear equations by the substitution method: mx - ny = m² + n² x + y = 2m

KnowledgeBoat · Accepted Answer

Given, mx - ny = m² + n² ......(i) x + y = 2m .......(ii) From eqn. (ii) we get, x = 2m - y .......(iii) Substituting value of x from eqn. (iii) in eqn. (i) we get, ⟹ m(2m - y) - ny = m² + n² ⟹ 2m² - my - ny = m² + n² ⟹ 2m² - m² - n² = my + ny ⟹ m² - n² = y(m + n) ⟹ y = = (m - n). Substituting value of y in eqn. (iii) we get, x = 2m - y = 2m - (m - n) = 2m - m + n = m + n. Hence, x = m + n and y = m - n.

Mathematics

Solve the following system of simultaneous linear equations by the substitution method:
mx - ny = m² + n²
x + y = 2m

Linear Equations

Related Questions

Solve the following system of simultaneous linear equations by the substitution method:
2x + 3y = 23
5x - 20 = 8y

Mathematics

Solve the following system of simultaneous linear equations by the substitution method:mx - ny = m2 + n2x + y = 2m

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Solve the following system of simultaneous linear equations by the substitution method:2x + 3y = 235x - 20 = 8y

Solve the following system of simultaneous linear equations by the substitution method:
mx - ny = m² + n²
x + y = 2m

Solve the following system of simultaneous linear equations by the substitution method:
2x + 3y = 23
5x - 20 = 8y