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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