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Find an ordered pair(x,y)  that solves the system: \(\begin{align*} 2x - 3y &= -3.2 - 0.2x + 0.1y,\\ x &= 0.6x - y + 8.8 \end{align*}\)

 May 29, 2019
 #1
avatar+18274 
+2

Gather like terms in the two equations to get :

2.2x - 3.1y = -3.2               (edited here due to error)

.4x+y = 8.8             Multily this equation by 3.1

1.24 +3.1 y = 27.28     and add this to the first equation to get

3.44x = 24.08      x= 7 

 

Sub this in to one of the original equations to find y = 6

 May 29, 2019
edited by ElectricPavlov  May 30, 2019
 #2
avatar+8095 
+3

Simplify first equation:

 

2x - 3y  =  -3.2 - 0.2x + 0.1y

                                                Add  0.2x  to both sides of the equation.

2.2x - 3y  =  -3.2 + 0.1y

                                                Add  3y  to both sides.

2.2x  = 3.1y  - 3.2

 

Simplify second equation:

 

x  =  0.6x - y + 8.8

                                      Add  y  to both sides of the equation.

x + y  =  0.6x + 8.8

                                      Subtract  x  from both sides.

y  =  -0.4x + 8.8

 

Substitute  -0.4x + 8.8  in for  y  in the first equation and solve for  x .

 

2.2x  =  3.1( -0.4x + 8.8 ) - 3.2

                                                     Distribute  3.1  to the terms in parenthesees.

2.2x  =  -1.24x + 27.28 - 3.2

                                                     Add  1.24x  to both sides.

2.2x + 1.24x =  27.28 - 3.2

                                                     Combine like terms.

3.44x  =  24.08

                                                     Divide both sides by  3.44

x  =  7

 

Substitute  7  in for  x  in the second equation to find  y .

 

y  =  -0.4( 7 ) + 8.8

 

y  =  6

 

Check:  https://www.desmos.com/calculator/f2brxhi1we

 May 29, 2019

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