# Solve the set of equations: −0.9848HI − 0.5736JH = 257.22 and −0.1736HI − 0.8192JH = −1060.8.

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### 2 Answers

The system of equations to be solved is

−0.9848HI − 0.5736JH = 257.22 ...(1)

−0.1736HI − 0.8192JH = −1060.8 ...(2)

where HI and JH are the variables

0.1736*(1) - 0.9848*(2)

=> -0.17096128HI + 0.17096128HI - 0.09957696JH + 0.80674816JH = 1089.329232

=> JH = 1540.4040384

Substitute JH in (1)

=> −0.9848HI − 0.5736*1540.4040384 = 257.22

=> HI = -(257.22 + 0.5736*1540.4040384)/0.9848

=> HI = -1158.403489

**The required values of the variables are JH = 1504.4040384 and HI = -1158.403489**

You should solve the system for HI and JH.

Use elimination method to remove the unknown HI.

Multiply the first equation by the coefficient of HI from the second equation. Multiply the second equation by the negative coefficient of HI from the first equation.

-0.1736(−0.9848HI − 0.5736JH) = -0.1736*257.22 =>

=> 0.17096128HI + 0.09957696JH = -44.653392

0.9848( −0.1736HI − 0.8192JH) = 0.9848*(-1060.8)=>

=> -0.17096128HI - 0.80674816JH = - 1044.67584

Adding the new equations yields:

-0.7071712JH = -1089.329232 => JH = -1089.329232/-0.7071712

JH = 1540.4038

Replace the value of JH in any of the two equations.

-0.9848HI - 0.5736*1540.4038 = 257.22

Adding 0.5736*1540.4038 = 883.5756 both sides yields:

−0.9848HI = 257.22 + 883.5756

−0.9848HI = 1140.7956

Dividing by -0.9848 yields:

HI = - 1140.7956/0.9848 => HI = - 1158.4033

**The solutions of the simultaneous equations are: HI = - 1158.4033 and JH = 1540.4038.**