Find the y-value of the solution below. x+y+z=7 y-7z=-35 2x-5y+2z=14

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to solve the system of equations, hence you may use the second equation to write y in terms of z such that:

`y = 7z - 35`

You may substitute `7z - 35`  for y in the first and the third equations such that:

`x + 7z - 35 + z = 7`

Collecting like terms yields:

`x + 8z = 7 + 35 =gt x + 8z = 42`

`2x - 5(7z - 35) + 2z = 14`

You need to open the brackets such that:

`2x - 35z + 175 + 2z = 14`

Collecting like terms yields:

`2x - 33z = 14 - 175`

`2x - 33z = -161`

You need to solve for x and z the system of equations:

`x + 8z = 42`

`2x - 33z = -161`

You need to multiply the first equation `x + 8z = 42 ` by -2 such that:

`-2x - 16z = -84`

You need to add the equation `-2x - 16z = -84`  to `2x - 33z = -161`  such that:

`2x - 33z- 2x - 16z= -161 - 84`

`-49z = -245 =gt z = 5`

Substituting 5 for z in `y = 7z - 35`  yields:

`y = 7*5 - 35 =gt y = 35- 35 =gt y = 0`

Hence, evaluating the y value yields y = 0.

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