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6.5 – Applying Systems of Linear Equations
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Ex x + 4y = -25 2x – 3y = 6
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” OR Eliminate “y”
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x”
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x”
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Ex [3x + 4y = -25] -3[2x – 3y = 6] Eliminate “x”
![Ex. 1 2[3x + 4y = -25] -3[2x – 3y = 6] Eliminate x](http://slideplayer.com/slide/7600957/25/images/6/Ex.+1+2%5B3x+%2B+4y+%3D+-25%5D+-3%5B2x+%E2%80%93+3y+%3D+6%5D+Eliminate+x.jpg "Ex. 1 2[3x + 4y = -25] -3[2x – 3y = 6] Eliminate x")
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Ex [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 = x +9y = -18](http://slideplayer.com/slide/7600957/25/images/7/Ex.+1+2%5B3x+%2B+4y+%3D+-25%5D+-3%5B2x+%E2%80%93+3y+%3D+6%5D+Eliminate+x+6x+%2B+8y+%3D+x+%2B9y+%3D+-18.jpg "Ex. 1 2[3x + 4y = -25] -3[2x – 3y = 6] Eliminate x 6x + 8y = x +9y = -18")
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Ex [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 = x +9y = -18](http://slideplayer.com/slide/7600957/25/images/8/Ex.+1+2%5B3x+%2B+4y+%3D+-25%5D+-3%5B2x+%E2%80%93+3y+%3D+6%5D+Eliminate+x+6x+%2B+8y+%3D+x+%2B9y+%3D+-18.jpg "Ex. 1 2[3x + 4y = -25] -3[2x – 3y = 6] Eliminate x 6x + 8y = x +9y = -18")
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = -18 17y = -68
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = y = -68
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = y = -68 y = -4
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” 6x + 8y = -50 -6x +9y = -18 17y = -68 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” OR Eliminate “y” 6x + 8y = -50 -6x +9y = -18 17y = -68 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” OR Eliminate “y” 6x + 8y = -50 -6x +9y = -18 17y = -68 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
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Ex [3x + 4y = -25] 4[2x – 3y = 6] Eliminate “x” OR Eliminate “y” 6x + 8y = -50 -6x +9y = -18 17y = -68 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
![Ex. 1 3[3x + 4y = -25] 4[2x – 3y = 6] Eliminate x OR Eliminate y 6x + 8y = x +9y = -18.](http://slideplayer.com/slide/7600957/25/images/15/Ex.+1+3%5B3x+%2B+4y+%3D+-25%5D+4%5B2x+%E2%80%93+3y+%3D+6%5D+Eliminate+x+OR+Eliminate+y+6x+%2B+8y+%3D+x+%2B9y+%3D+-18..jpg "17y = y = -4. 3x + 4y = x + 4(-4) = x – 16 = x = x = -3. (-3, -4)")
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Ex [3x + 4y = -25] 4[2x – 3y = 6] Eliminate “x” OR Eliminate “y” 6x + 8y = x + 12y = -75 -6x +9y = x – 12y = 24 17y = -68 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
![Ex. 1 3[3x + 4y = -25] 4[2x – 3y = 6] Eliminate x OR Eliminate y 6x + 8y = -50 9x + 12y = -75.](http://slideplayer.com/slide/7600957/25/images/16/Ex.+1+3%5B3x+%2B+4y+%3D+-25%5D+4%5B2x+%E2%80%93+3y+%3D+6%5D+Eliminate+x+OR+Eliminate+y+6x+%2B+8y+%3D+-50+9x+%2B+12y+%3D+-75..jpg "-6x +9y = -18 8x – 12y = y = y = -4. 3x + 4y = x + 4(-4) = x – 16 = x = x = -3. (-3, -4)")
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” OR Eliminate “y” 6x + 8y = x + 12y = -75 -6x +9y = x – 12y = 24 17y = x = -51 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” OR Eliminate “y” 6x + 8y = x + 12y = -75 -6x +9y = x – 12y = 24 17y = x = -51 y = -4 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” OR Eliminate “y” 6x + 8y = x + 12y = -75 -6x +9y = x – 12y = 24 17y = x = -51 y = x = -3 3x + 4y = -25 3x + 4(-4) = -25 3x – 16 = -25 3x = -9 x = -3 (-3, -4)
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Ex x + 4y = -25 2x – 3y = 6 Eliminate “x” OR Eliminate “y” 6x + 8y = x + 12y = -75 -6x +9y = x – 12y = 24 17y = x = -51 y = x = -3 3x + 4y = x + 4y = -25 3x + 4(-4) = (-3) + 4y = -25 3x – 16 = y = -25 3x = y = -16 x = y = -4 (-3, -4)
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Ex. 2 Determine the best method to solve the system of equations
Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12 x + 2y = 14
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Ex. 2 Determine the best method to solve the system of equations
Ex. 2 Determine the best method to solve the system of equations. Then solve the system. 4x – 3y = 12 -4[ x + 2y = 14]
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Ex. 2 Determine the best method to solve the system of equations
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
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Ex. 2 Determine the best method to solve the system of equations
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
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Ex. 2 Determine the best method to solve the system of equations
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 = x – 3(4) = 12 -4x – 8y = x – 12 = 12 -11y = x = 24 y = x = 6 (6,4)
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Ex.3 3x – 7y = -14 5x + 2y = 45
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Ex x – 7y = -14 5x + 2y = 45 2[3x – 7y = -14] [3x – 7y = -14] 7[5x + 2y = 45] -3[5x + 2y = 45] 6x – 14y = x – 35y = -70 35x + 14y = x – 6y = -135 41x = y = -205 x = y = 5 3x – 7y = x – 7y = -14 3(7) – 7y = x – 7(5) = -14 21 – 7y = x – 35 = -14 -7y = x = 21 y = (7,5) x = 7
![Ex.3 3x – 7y = -14 5x + 2y = 45. 2[3x – 7y = -14] 5[3x – 7y = -14] 7[5x + 2y = 45] -3[5x + 2y = 45]](http://slideplayer.com/slide/7600957/25/images/27/Ex.3+3x+%E2%80%93+7y+%3D+-14+5x+%2B+2y+%3D+45.+2%5B3x+%E2%80%93+7y+%3D+-14%5D+5%5B3x+%E2%80%93+7y+%3D+-14%5D+7%5B5x+%2B+2y+%3D+45%5D+-3%5B5x+%2B+2y+%3D+45%5D.jpg "6x – 14y = x – 35y = x + 14y = x – 6y = x = y = x = 7 y = 5. 3x – 7y = -14 3x – 7y = (7) – 7y = -14 3x – 7(5) = – 7y = -14 3x – 35 = y = -35 3x = 21. y = 5 (7,5) x = 7.")
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