# For what values of x, y, and z are 2 - 2x = y, -3z + 4x = 0 and 9z - 6 = -4y true?

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Given the system:

2 - 2x = y.............(1)

-3z + 4x = 0.............(2)

9z - 6 = -4y...........(3)

To solve we will use the substitution method.

We will substitute (1) into (3).

==> 9z - 6 = -4y

==> 9z - 6 = -4 (2-2x)

==> 9z - 6 = -8 + 8x

==> 9z - 8x = -2.............(4)

Now we will multiply (2) by 2 and add to (4).

==> 2*(2)

-6z + 8x = 0

==> 2*(2) + (4)

==> 3z = -2

**==> z= -2/3**

Now we will substitute into (2) to find x.

==> -3z + 4x = 0

==> -3*-2/3 + 4x = 0

==> 2 + 4x = 0

==> 4x = -2

**==> x= -1/2**

Now we will substitute into (1) to find y.

==> y= 2 - 2x = 2- 2(-1/2)

==> y= 2 + 1 = 3

**==> y= 3**

**Then the answer is: **

**x= -1/2, y= 3, and z = -2/3**

We have to find x, y and z using the following equations:

2-2x=y...(1)

-3z+4x=0...(2)

9z-6=-4y...(3)

From (1) we get y = 2 - 2x

substitute this in (3)

9z - 6 = -4(2 - 2x)

=> 9z - 6 = -8 + 8x

=> 9z = 8x - 2

Substitute this in (2)

-3z + 4x = 0

=> -3 ( 8x/9 - 2/9) + 4x = 0

=> -24x / 9 + 6/9 + 4x = 0

=> -24x + 6 + 36x = 0

=> 12x = -6

=> x = -1/2

9z = 8x - 2

=> 9z = -4 - 2

=> z = -6/9 = -2/3

y = 2 - 2x

=> 2 + 1

=> y = 3

**Therefore x = -1/2 , y = 3 and z = -2/3**

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