Finite Math Examples

$x + 3 y - 2 z = 0$ , $2 x + 4 z = 2$ , $4 x + 6 y = 2$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $3 y$ from both sides of the equation.

$x - 2 z = - 3 y$

$2 x + 4 z = 2$

$4 x + 6 y = 2$

Step 1.2

Add $2 z$ to both sides of the equation.

$x = - 3 y + 2 z$

$2 x + 4 z = 2$

$4 x + 6 y = 2$

$x = - 3 y + 2 z$

$2 x + 4 z = 2$

$4 x + 6 y = 2$

Step 2

Replace all occurrences of $x$ with $- 3 y + 2 z$ in each equation.

Tap for more steps...

Step 2.1

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

$2 (- 3 y + 2 z) + 4 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $2 (- 3 y + 2 z) + 4 z$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$2 (- 3 y) + 2 (2 z) + 4 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

Step 2.2.1.1.2

Multiply $- 3$ by $2$ .

$- 6 y + 2 (2 z) + 4 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

Step 2.2.1.1.3

Multiply $2$ by $2$ .

$- 6 y + 4 z + 4 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

$- 6 y + 4 z + 4 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

Step 2.2.1.2

Add $4 z$ and $4 z$ .

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

$4 x + 6 y = 2$

Step 2.3

Replace all occurrences of $x$ in $4 x + 6 y = 2$ with $- 3 y + 2 z$ .

$4 (- 3 y + 2 z) + 6 y = 2$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $4 (- 3 y + 2 z) + 6 y$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

Apply the distributive property.

$4 (- 3 y) + 4 (2 z) + 6 y = 2$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

Step 2.4.1.1.2

Multiply $- 3$ by $4$ .

$- 12 y + 4 (2 z) + 6 y = 2$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

Step 2.4.1.1.3

Multiply $2$ by $4$ .

$- 12 y + 8 z + 6 y = 2$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

$- 12 y + 8 z + 6 y = 2$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

Step 2.4.1.2

Add $- 12 y$ and $6 y$ .

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$

$- 6 y + 8 z = 2$

$x = - 3 y + 2 z$