kase12
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Help please! 99 Points!
Solve the system of equations using the Linear Combination Method.
5. 4x-9y=1
-4x+6y=-2

6. 3x-2y=14
2x+2y=6

Solve using any method
7. 4x+3y=29
5x+2y=24

8. -4x-2y=14
-10x+7y=-25



Respuesta :

AnimeBrainly
Combination method: add the two equations together

5)      4x-9y=1                                    6)  3x - 2y = 14
  +( - 4x+6y=-2 )                                 + (2x + 2y = 6)
----------------------                                 -------------------
         0 - 5y = -1                                      5x + 0 = 20


-5y = -1                                                   5x = 20

isolate the y                                            isolate the x

-5y / -5 = -1/-5                                        5x/5 = 20/5

y = 1/5                                                     x = 4

4x-9y=1                                                   3x - 2y = 14
4x - 9(1/5) = 1                                         3(4) - 2y = 14
4x - 9/5 = 1                                              12 - 2y = 14
4x - 9/5 (+9/5) = 1 (+9/5)                         12 (-12) - 2y = 14 (-12)
4x = 14/5                                                -2y = 2
4x/4 = 14/5(/4)                                        -2y(/-2) = 2(/-2)
x = 14/20                                                 y = -1


Elimination method

7)  4x + 3y = 29 + (5x + 2y = 24)
   eliminate one of the variables by multiply the number to both sides

2 (4x + 3y = 29) + 3 (5x + 2y = 24)

    8x + 6y = 58  
-( 15x + 6y = 72)
----------------------
    -7x   = - 14
-7x/-7 = -14/-7

x = 2

4(x) + 3y = 29
4(2) + 3y = 29
3y + 8 = 29
3y + 8 (-8) = 29 (-8)
3y = 21
3y/3 = 21/3

y = 7


8)   like #7, you must   eliminate one of the variables by multiply the number to both sides

-4x - 2y = 14
-10x + 7y = -25

7(-4x - 2y = 14)
-2(-10x + 7y = -25)

-28x - 14y = 98
- (20x -14y = -25)
-----------------------
-48x          = 123
-48x/-48 = 123/-48
x = -2.56

-4(-2.56) - 2y = 14
10.24 - 2y = 14
10.24(-10.24) - 2y = 14 (-10.24)
-2y = 3.76
-2y/-2 = 3.76/-2
y = -1.88







hope this helps





Astute
Hey there,

As seeing the (mathematics's above) I would be more willing list the steps, but to just tell you the answer.

[tex]\boxed{y = -2.56}[/tex] and also [tex]\boxed{y =1.88}[/tex]

Hope this helps.

~Jurgen



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