Solve the System of Equations 2x+4y-z=-7 3y+7z=38 -2z=-10

$2 x + 4 y - z = - 7$ $3 y + 7 z = 38$ $- 2 z = - 10$

Step 1

Divide each term in $- 2 z = - 10$ by $- 2$ and simplify.

Divide each term in $- 2 z = - 10$ by $- 2$ .

$\frac{- 2 z}{- 2} = \frac{- 10}{- 2}$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 z}{- 2} = \frac{- 10}{- 2}$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

Divide $z$ by $1$ .

$z = \frac{- 10}{- 2}$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

$z = \frac{- 10}{- 2}$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

$z = \frac{- 10}{- 2}$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$z = 5$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

$z = 5$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

$z = 5$

$2 x + 4 y - z = - 7$

$3 y + 7 z = 38$

Step 2

Replace all occurrences of $z$ with $5$ in each equation.

Replace all occurrences of $z$ in $2 x + 4 y - z = - 7$ with $5$ .

$2 x + 4 y - (5) = - 7$

$z = 5$

$3 y + 7 z = 38$

Simplify the left side.

Multiply $- 1$ by $5$ .

$2 x + 4 y - 5 = - 7$

$z = 5$

$3 y + 7 z = 38$

$2 x + 4 y - 5 = - 7$

$z = 5$

$3 y + 7 z = 38$

Replace all occurrences of $z$ in $3 y + 7 z = 38$ with $5$ .

$3 y + 7 (5) = 38$

$2 x + 4 y - 5 = - 7$

$z = 5$

Simplify the left side.

Multiply $7$ by $5$ .

$3 y + 35 = 38$

$2 x + 4 y - 5 = - 7$

$z = 5$

$3 y + 35 = 38$

$2 x + 4 y - 5 = - 7$

$z = 5$

$3 y + 35 = 38$

$2 x + 4 y - 5 = - 7$

$z = 5$

Step 3

Solve for $y$ in $3 y + 35 = 38$ .

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

Subtract $35$ from both sides of the equation.

$3 y = 38 - 35$

$2 x + 4 y - 5 = - 7$

$z = 5$

Subtract $35$ from $38$ .

$3 y = 3$

$2 x + 4 y - 5 = - 7$

$z = 5$

$3 y = 3$

$2 x + 4 y - 5 = - 7$

$z = 5$

Divide each term in $3 y = 3$ by $3$ and simplify.

Divide each term in $3 y = 3$ by $3$ .

$\frac{3 y}{3} = \frac{3}{3}$

$2 x + 4 y - 5 = - 7$

$z = 5$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{3}{3}$

$2 x + 4 y - 5 = - 7$

$z = 5$

Divide $y$ by $1$ .

$y = \frac{3}{3}$

$2 x + 4 y - 5 = - 7$

$z = 5$

$y = \frac{3}{3}$

$2 x + 4 y - 5 = - 7$

$z = 5$

$y = \frac{3}{3}$

$2 x + 4 y - 5 = - 7$

$z = 5$

Simplify the right side.

Divide $3$ by $3$ .

$y = 1$

$2 x + 4 y - 5 = - 7$

$z = 5$

$y = 1$

$2 x + 4 y - 5 = - 7$

$z = 5$

$y = 1$

$2 x + 4 y - 5 = - 7$

$z = 5$

$y = 1$

$2 x + 4 y - 5 = - 7$

$z = 5$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

Replace all occurrences of $y$ in $2 x + 4 y - 5 = - 7$ with $1$ .

$2 x + 4 (1) - 5 = - 7$

$y = 1$

$z = 5$

Simplify the left side.

Simplify $2 x + 4 (1) - 5$ .

Multiply $4$ by $1$ .

$2 x + 4 - 5 = - 7$

$y = 1$

$z = 5$

Subtract $5$ from $4$ .

$2 x - 1 = - 7$

$y = 1$

$z = 5$

$2 x - 1 = - 7$

$y = 1$

$z = 5$

$2 x - 1 = - 7$

$y = 1$

$z = 5$

$2 x - 1 = - 7$

$y = 1$

$z = 5$

Step 5

Solve for $x$ in $2 x - 1 = - 7$ .

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

Add $1$ to both sides of the equation.

$2 x = - 7 + 1$

$y = 1$

$z = 5$

Add $- 7$ and $1$ .

$2 x = - 6$

$y = 1$

$z = 5$

$2 x = - 6$

$y = 1$

$z = 5$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

$y = 1$

$z = 5$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

$y = 1$

$z = 5$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

$y = 1$

$z = 5$

$x = \frac{- 6}{2}$

$y = 1$

$z = 5$

$x = \frac{- 6}{2}$

$y = 1$

$z = 5$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

$y = 1$

$z = 5$

$x = - 3$

$y = 1$

$z = 5$

$x = - 3$

$y = 1$

$z = 5$

$x = - 3$

$y = 1$

$z = 5$

Step 6

Solve the system of equations $x = - 3 y = 1 z = 5$ .

$x = - 3 y = 1 z = 5$

Step 7

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 3, 1, 5)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 3, 1, 5)$

Equation Form:

$x = - 3, y = 1, z = 5$

Solve the System of Equations 2x+4y-z=-7 3y+7z=38 -2z=-10

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