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 - 3y - z = -1
x - 4y + 3z = -11
2x + 9y + 3z = -13

-11y + 5z = 21
y + 9z = 9

5y - 7z = 21
17y - 3z = 9

7x - 13y = -14
8x + 0y = -16

-5x +5y = -8
-4x + 18z = -10

I don't understand how to get these at all..

Question

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 - 3y - z = -1
x - 4y + 3z = -11
2x + 9y + 3z = -13

-11y + 5z = 21
y + 9z = 9

	5y - 7z = 21
17y - 3z = 9

	7x - 13y = -14
8x + 0y = -16

	-5x +5y = -8
-4x + 18z = -10

I don't understand how to get these at all..

mathstudent55 · Answer

In the first two choices, there is no x variable. That means they solved one equation for x and substituted that value of x into the other two. 
Look at the three equations, the second can be easily solved for x.
x - 4y + 3z = -11
x = 4y - 3z - 11
Now substitute this value of x into the first and third equations.

First equation:
2x - 3y - z = -1
2(4y - 3z - 11) - 3y - z = -1
8y - 6z - 22 - 3y - z = -1
5y - 7z = 21
Notice the above equation is included in choice B.

Third equation:
2x + 9y + 3z = -13
2(4y - 3z - 11) + 9y + 3z = -13
8y - 6z - 22 + 9y + 3z = -13
17y -3z = 9
This is the other equation of choice B.

anonymous · Answer

thanks you stated it so clearly! thanks so much

mathstudent55 · Answer

you're welcome