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tommy_gun tommy_gun
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Posts: 83
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11 years ago
If you were to use the substitution method to solve the following system, choose the new system of equations that would result if x was isolated in the second equation.

2x + 5y ? 2z = ?1
x + 3y + z = ?2
3x ? 2y + 3z = ?17
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wrote...
#1
11 years ago
sum first and second and get a new equation.then subtract from third equation and find y.After that it is easy.
wrote...
#2
11 years ago
Hi,

2x + 5y ? 2z = ?1
x + 3y + z = ?2
3x ? 2y + 3z = ?17

x + 3y + z = ?2

x = -2 - 3y - z


2(-2 - 3y - z) + 5y ? 2z = ?1
 
-4 - 6y - 2z + 5y - 2z = -1

-y - 4z = 3


3(-2 - 3y - z) ? 2y + 3z = ?17

-6 - 9y - 3z - 2y + 3z = -17

-11y = -11

 y = 1

If y = 1 and -y - 4z = 3, then:

-1 - 4z = 3

-4z = 4

 z = -1

If y = 1 and z = -1, then:

2x + 5y - 2z = -1

2x + 5(1) - 2(-1) = -1

2x + 5 + 2 = -1

2x + 7 = -1

2x = -8

 x = -4

 (-4, 1, -1) <==ANSWER

I hope that helps!! :-)
RJW
wrote...
#3
11 years ago
Isolate x in the 2nd equation:

x = -2 - 3y - z

Substitute in 1st and 3rd equations:

2(-2 - 3y - z) + 5y - 2z = -1
3(-2 - 3y - z) - 2y + 3z = -17

Expand each one and rearrange the terms to make everything look neat, and you are done.

Note that the question only asks you to show the two equations (showing only y and z, no x); the question does not ask you to actually solve.
wrote...
#4
11 years ago
x = -3y - z - 2
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