Solve the simultaneous equations. x/3 + y/4 = 4; x/2 - y/4=1

Question

Solve the simultaneous equations. \(\frac{x}{3}\)+ \(\frac{y}{4}\)= 4;  \(\frac{x}{2}\)- \(\frac{y}{4}\)= 1

x/3 + y/4 = 4; x/2 - y/4=1

Answer 1

 \(\frac{x}{3}\)+ \(\frac{y}{4}\)= 4

Multiplying both sides by 12,

 4x + 3y = 48 …(i)

  \(\frac{x}{2}\)- \(\frac{y}{4}\)= 1

Multiplying both sides by 8,

4x – 2y = 8 …..(ii) 

Subtracting equation (ii) from (i),

∴ y = 8 

Substituting y = 8 in equation (ii),

 4x – 2y = 8 

∴ 4x – 2(8) = 8 

∴ 4x – 16 = 8 

∴ 4x = 8+ 16 

∴ 4x = 24 

∴ x = \(\frac{24}{4}\)

∴ x = 6 

∴ (6, 8) is the solution of the given equations.