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Chapter Ten
Systems of Linear EquationsPrepared by: Richard Mitchell Humber College
10
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CASE STUDY
10.1-Systems of Two Linear Equations310.1-EXAMPLE 8-Page 267Solve by the addition-subtraction method:
Add
10.1-EXAMPLE 9-Page 267Solve by the addition-subtraction method:
AddMultiply by 310.1-EXAMPLE 10-Page 268Solve by the addition-subtraction method:
Multiply by 3
AddMultiply by 410.1-EXAMPLE 12-Page 269Solve by the substitution method:
Substitute (5x 17) into the first equation (instead of y ).
10.2 - Other Systems of Equations
810.2-EXAMPLE 15-Page 273Solve for x and y:
Multiply by 4
AddMultiply by 610.2-EXAMPLE 16-Page 273Solve for x and y:
Multiply by 3xy
SubtractMultiply by 2xy
10.2-EXAMPLE 17-Page 274Solve for x and y:
Multiply by 12
SubtractMultiply by 15
Multiply by 9Multiply by 8
10.2-EXAMPLE 20-Page 275Solve for x and y using Eqs. 63:
Re-write both equations.Substitute values given for a, b and c into Eq. 63.
10.3 - Word Problems with Two Unknowns1310.3-EXAMPLE 22-Page 278 (Mixture Problem)AMOUNTof GasoholPERCENT ofAlcoholAMOUNT of ALCOHOLMixtureAMixtureBTOTALSx=0.050.120.10(1000)xy0.05 (x)0.12 (y)
Equations
10000.10Multiply by 100Multiply by 5
Subtract
10.3-EXAMPLE 23-Page 279 (Work Problem)
Equations
Multiply by 4.0Multiply by 6.5
Subtract
10.3-EXAMPLE extra
Substitute (1.75C) into the first equation (instead of H ).
10.3-EXAMPLE extraUse Kirchhoffs Law to write a pair of equations for the circuit shown below and solve the equations for I1 and I2 .
Multiply by 207
SubtMultiply by 363
10.4 - Systems of Three Linear Equations
1810.4-EXAMPLE 25-Page 286Solve for x, y and z:
Multiply by 2
SubtractMultiply by 3
Multiply by 3
SubtractMultiply by 5
Multiply by 2
AddMultiply by 5(cont)10.4-EXAMPLE 25-Page 286Solve for x, y and z:
10.4-EXAMPLE 26-Page 287Solve by the substitution method:
Substitute (x - 4) into the last equation for y and (8 x) into the last equation for z.
Re-write the first two equations in terms of x such that y = (x 4) and z = (8 x).
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