Solve the System of Equations y+z=4 y-z=8

$y + z = 4$ $y - z = 8$

Subtract $z$ from both sides of the equation.

$y = 4 - z$

$y - z = 8$

Replace all occurrences of $y$ with $4 - z$ in each equation.

Replace all occurrences of $y$ in $y - z = 8$ with $4 - z$ .

$(4 - z) - z = 8$

$y = 4 - z$

Simplify the left side.

Subtract $z$ from $- z$ .

$4 - 2 z = 8$

$y = 4 - z$

$4 - 2 z = 8$

$y = 4 - z$

$4 - 2 z = 8$

$y = 4 - z$

Solve for $z$ in $4 - 2 z = 8$ .

Move all terms not containing $z$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$- 2 z = 8 - 4$

$y = 4 - z$

Subtract $4$ from $8$ .

$- 2 z = 4$

$y = 4 - z$

$- 2 z = 4$

$y = 4 - z$

Divide each term in $- 2 z = 4$ by $- 2$ and simplify.

Divide each term in $- 2 z = 4$ by $- 2$ .

$\frac{- 2 z}{- 2} = \frac{4}{- 2}$

$y = 4 - z$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 z}{- 2} = \frac{4}{- 2}$

$y = 4 - z$

Divide $z$ by $1$ .

$z = \frac{4}{- 2}$

$y = 4 - z$

$z = \frac{4}{- 2}$

$y = 4 - z$

$z = \frac{4}{- 2}$

$y = 4 - z$

Simplify the right side.

Divide $4$ by $- 2$ .

$z = - 2$

$y = 4 - z$

$z = - 2$

$y = 4 - z$

$z = - 2$

$y = 4 - z$

$z = - 2$

$y = 4 - z$

Replace all occurrences of $z$ with $- 2$ in each equation.

Replace all occurrences of $z$ in $y = 4 - z$ with $- 2$ .

$y = 4 - (- 2)$

$z = - 2$

Simplify the right side.

Simplify $4 - (- 2)$ .

Multiply $- 1$ by $- 2$ .

$y = 4 + 2$

$z = - 2$

Add $4$ and $2$ .

$y = 6$

$z = - 2$

$y = 6$

$z = - 2$

$y = 6$

$z = - 2$

$y = 6$

$z = - 2$

List all of the solutions.

$y = 6, z = - 2$

Solve the System of Equations y+z=4 y-z=8

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