Solve the System of Equations x+2z=30 y+z=12 z=1

$x + 2 z = 30$ $y + z = 12$ $z = 1$

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

Replace all occurrences of $z$ in $x + 2 z = 30$ with $1$ .

$x + 2 (1) = 30$

$z = 1$

$y + z = 12$

Simplify the left side.

Multiply $2$ by $1$ .

$x + 2 = 30$

$z = 1$

$y + z = 12$

$x + 2 = 30$

$z = 1$

$y + z = 12$

Replace all occurrences of $z$ in $y + z = 12$ with $1$ .

$y + 1 = 12$

$x + 2 = 30$

$z = 1$

Simplify the left side.

Remove parentheses.

$y + 1 = 12$

$x + 2 = 30$

$z = 1$

$y + 1 = 12$

$x + 2 = 30$

$z = 1$

$y + 1 = 12$

$x + 2 = 30$

$z = 1$

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

Subtract $1$ from both sides of the equation.

$y = 12 - 1$

$x + 2 = 30$

$z = 1$

Subtract $1$ from $12$ .

$y = 11$

$x + 2 = 30$

$z = 1$

$y = 11$

$x + 2 = 30$

$z = 1$

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

Subtract $2$ from both sides of the equation.

$x = 30 - 2$

$y = 11$

$z = 1$

Subtract $2$ from $30$ .

$x = 28$

$y = 11$

$z = 1$

$x = 28$

$y = 11$

$z = 1$

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

$(28, 11, 1)$

The result can be shown in multiple forms.

Point Form:

$(28, 11, 1)$

Equation Form:

$x = 28, y = 11, z = 1$

Solve the System of Equations x+2z=30 y+z=12 z=1

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