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Substitution Method











































Solve the system of two equations by using the substitution method.

If a unique solution does not exist, explain whether the system has many solutions or no solution.

y = 4x – 7

y = 9x - 8

Comments for Substitution Method

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Jul 10, 2013
Solve for x and y
by: Staff


Answer

Part I


4x – 7 can be substituted for the y in the second equation:


Or


9x – 8 can be substituted for the y in the first equation.

………………………………………………………………..

I will substitute 4x – 7 for the y in the second equation


y = 9x – 8

4x – 7 = 9x – 8


Substitute 4x – 7 for y





The second equation now has only one variable, x.


Solve for x:

4x – 7 = 9x – 8


Subtract -4x from both sides of the equation

4x – 7 – 4x = 9x – 8 – 4x

4x – 4x – 7 = 9x – 4x – 8

0 – 7 = 5x – 8

– 7 = 5x – 8


Solve for x.  Begin by subtracting 4x from both sides of the equation.




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Jul 10, 2013
Solve for x and y
by: Staff


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Part II



Add 8 to each side of the equation

– 7 + 8 = 5x – 8 + 8

1 = 5x + 0

1 = 5x


add 8 to both sides of the equation




Divide each side of the equation by 5

1 / 5 = 5x / 5

1 / 5 = x

x = 1 / 5

x = 0.2


divide both sides of the equation by 5





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Jul 10, 2013
Solve for x and y
by: Staff


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Part III


Solve for y

Substitute 1 / 5 for x in either equation

y = 9x – 8

y = 9*(1 / 5) – 8

y = 9 / 5 – 8

y = 9 / 5 – 8 * (5 / 5)

y = 9 / 5 – 40 / 5

y = (9 – 40)/ 5

y = – 31/ 5

y = – 6.2


Substitute 1 / 5 for x and then compute y




the final answer is:

x = 0.2

y = – 6.2


Linear System of two equations solved by substitution – final answer





………………………………………………………………..

Check the final answer by substituting the values of x and y in either equation:

y = 4x – 7

x = 0.2

y = – 6.2

– 6.2 = 4 * 0.2 – 7

– 6.2 = 0.8 – 7

– 6.2 = – 6.2, OK → x = 0.2 and y = – 6.2 is a valid solution





Thanks for writing.

Staff
www.solving-math-problems.com


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