Solve the System of Equations x+4y+z=12 y-3z=-7 z=3

$x + 4 y + z = 12$ $y - 3 z = - 7$ $z = 3$

Replace all occurrences of $z$ with $3$ in each equation.

Replace all occurrences of $z$ in $x + 4 y + z = 12$ with $3$ .

$x + 4 y + 3 = 12$

$z = 3$

$y - 3 z = - 7$

Simplify the left side.

Remove parentheses.

$x + 4 y + 3 = 12$

$z = 3$

$y - 3 z = - 7$

$x + 4 y + 3 = 12$

$z = 3$

$y - 3 z = - 7$

Replace all occurrences of $z$ in $y - 3 z = - 7$ with $3$ .

$y - 3 \cdot 3 = - 7$

$x + 4 y + 3 = 12$

$z = 3$

Simplify the left side.

Multiply $- 3$ by $3$ .

$y - 9 = - 7$

$x + 4 y + 3 = 12$

$z = 3$

$y - 9 = - 7$

$x + 4 y + 3 = 12$

$z = 3$

$y - 9 = - 7$

$x + 4 y + 3 = 12$

$z = 3$

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

Add $9$ to both sides of the equation.

$y = - 7 + 9$

$x + 4 y + 3 = 12$

$z = 3$

Add $- 7$ and $9$ .

$y = 2$

$x + 4 y + 3 = 12$

$z = 3$

$y = 2$

$x + 4 y + 3 = 12$

$z = 3$

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x + 4 y + 3 = 12$ with $2$ .

$x + 4 (2) + 3 = 12$

$y = 2$

$z = 3$

Simplify the left side.

Simplify $x + 4 (2) + 3$ .

Multiply $4$ by $2$ .

$x + 8 + 3 = 12$

$y = 2$

$z = 3$

Add $8$ and $3$ .

$x + 11 = 12$

$y = 2$

$z = 3$

$x + 11 = 12$

$y = 2$

$z = 3$

$x + 11 = 12$

$y = 2$

$z = 3$

$x + 11 = 12$

$y = 2$

$z = 3$

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

Subtract $11$ from both sides of the equation.

$x = 12 - 11$

$y = 2$

$z = 3$

Subtract $11$ from $12$ .

$x = 1$

$y = 2$

$z = 3$

$x = 1$

$y = 2$

$z = 3$

Solve the system of equations $x = 1 y = 2 z = 3$ .

$x = 1 y = 2 z = 3$

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

$(1, 2, 3)$

The result can be shown in multiple forms.

Point Form:

$(1, 2, 3)$

Equation Form:

$x = 1, y = 2, z = 3$

Solve the System of Equations x+4y+z=12 y-3z=-7 z=3

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