# 6.5 – Applying Systems of Linear Equations

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6.5 – Applying Systems of Linear Equations. Ex. 1 3 x + 4 y = -25 2 x – 3 y = 6. Ex. 1 3 x + 4 y = -25 2 x – 3 y = 6 Eliminate “ x ” OR Eliminate “ y ”. Ex. 1 3 x + 4 y = -25 2 x – 3 y = 6 Eliminate “ x ”. Ex. 1 3 x + 4 y = -25 - PowerPoint PPT Presentation

### Text of 6.5 – Applying Systems of Linear Equations

• 6.5 Applying Systems of Linear Equations

• Ex. 1 3x + 4y = -252x 3y = 6

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x OR Eliminate y

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x

• Ex. 1 2[3x + 4y = -25] -3[2x 3y = 6]Eliminate x

• Ex. 1 2[3x + 4y = -25] -3[2x 3y = 6]Eliminate x 6x + 8y = -50-6x +9y = -18

• Ex. 1 2[3x + 4y = -25] -3[2x 3y = 6]Eliminate x 6x + 8y = -50-6x +9y = -18

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x 6x + 8y = -50 -6x +9y = -18 17y = -68

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x 6x + 8y = -50-6x +9y = -1817y = -68 17 17

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x 6x + 8y = -50-6x +9y = -1817y = -68 17 17 y = -4

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x 6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x OR Eliminate y6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x OR Eliminate y6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3[3x + 4y = -25] 4[2x 3y = 6]Eliminate x OR Eliminate y6x + 8y = -50 -6x +9y = -18 17y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3[3x + 4y = -25] 4[2x 3y = 6]Eliminate x OR Eliminate y6x + 8y = -509x + 12y = -75-6x +9y = -188x 12y = 2417y = -68 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x OR Eliminate y6x + 8y = -509x + 12y = -75-6x +9y = -188x 12y = 2417y = -6817x = -51 17 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x OR Eliminate y6x + 8y = -509x + 12y = -75-6x +9y = -188x 12y = 2417y = -6817x = -51 17 1717 17 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x OR Eliminate y6x + 8y = -509x + 12y = -75-6x +9y = -188x 12y = 2417y = -6817x = -51 17 1717 17 y = -4x = -33x + 4y = -25 3x + 4(-4) = -25 3x 16 = -25 +16 +16 3x = -9 3 3 x = -3 (-3, -4)

• Ex. 1 3x + 4y = -25 2x 3y = 6Eliminate x OR Eliminate y6x + 8y = -509x + 12y = -75-6x +9y = -188x 12y = 2417y = -6817x = -51 17 1717 17 y = -4x = -33x + 4y = -25 3x + 4y = -253x + 4(-4) = -25 3(-3) + 4y = -253x 16 = -25 -9 + 4y = -25 +16 +16 +9 +9 3x = -94y = -16 3 3 4 4 x = -3y = -4(-3, -4)

• Ex. 2 Determine the best method to solve the system of equations. Then solve the system.4x 3y = 12 x + 2y = 14

• Ex. 2 Determine the best method to solve the system of equations. Then solve the system.4x 3y = 12 -4[ x + 2y = 14]

• Ex. 2 Determine the best method to solve the system of equations. Then solve the system.4x 3y = 12 -4[ x + 2y = 14]

4x 3y = 12

• Ex. 2 Determine the best method to solve the system of equations. Then solve the system.4x 3y = 12 -4[ x + 2y = 14]

4x 3y = 12-4x 8y = -56

• Ex. 2 Determine the best method to solve the system of equations. Then solve the system.4x 3y = 12 -4[ x + 2y = 14]

4x 3y = 124x 3(4) = 12-4x 8y = -56 4x 12 = 12 -11y = -444x = 24 y = 4 x = 6

(6,4)

• Ex.33x 7y = -145x + 2y = 45

• Ex.3 3x 7y = -14 5x + 2y = 452[3x 7y = -14] 5[3x 7y = -14] 7[5x + 2y = 45] -3[5x + 2y = 45] 6x 14y = -28 15x 35y = -7035x + 14y = 315 -15x 6y = -135 41x = 287 -41y = -205 x = 7 y = 5 3x 7y = -14 3x 7y = -143(7) 7y = -14 3x 7(5) = -1421 7y = -14 3x 35 = -14-7y = -35 3x = 21 y = 5 (7,5) x = 7

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