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solve the system

by kaitie parker
(morgantown indiana US)











































Solve the system of linear equations for x and y

2x - 6y = -10

10x + 18y = -2

Use the addition method

Check the values of x and y by substituting the solutions into the original two equations.

Comments for solve the system

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Apr 18, 2011
Solve the Linear System
by: Staff


The question:

by Kaitie Parker
(Morgantown, Indiana, US)

2x-6y=-10
10x+18y=-2

The answer:

2x - 6y = -10
10x + 18y = -2


Use the addition method


Multiply each side of the 1st equation by (-5)

2x - 6y = -10

(-5)*(2x - 6y) = (-5)*(-10)

-10x + 30y = 50


Add the two equations together


-10x + 30y = 50
10x + 18y = -2
-----------------------
-10x + 30y +10x + 18y = 50 - 2

-10x + 30y +10x + 18y = 48


Combine like terms

-10x +10x + 30y + 18y = 48

0 + 30y + 18y = 48

30y + 18y = 48

48y = 48


Divide each side of the equation by 48

48y/48 = 48/48

48y/48 = 1

y*(48/48) = 1

y*(1) = 1

y = 1


Substitute 1 for y in one of the original equations, then solve for x


2x - 6y = -10

2x - 6*1 = -10

2x - 6 = -10

2x - 6 + 6 = -10 + 6

2x - 6 + 6 = -4

2x + 0 = -4


Divide each side of the equation by 2

2x = -4

2x/2 = -4/2

2x/2 = -2

x*(2/2) = -2

x*(1) = -2

x = -2


the final answer is: x = -2, y = 1



Check the work. Substitute -2 for x and 1 for y in the original two equations.

2x - 6y = -10

2*(-2) - 6*1 = -10

-4 - 6 = -10

-10 = -10, correct


10x + 18y = -2

10*(-2) + 18*1 = -2

-20 + 18 = -2

-2 = -2, correct


The values of x = -2 and y = 1 are valid solutions in both of the original equations. This verifies that these values are correct solutions.



Thanks for writing.


Staff
www.solving-math-problems.com


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