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

justaguide | College Teacher | (Level 2) Distinguished Educator

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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

sciencesolve | Teacher | (Level 3) Educator Emeritus

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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

-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.