Finite Math Examples

$x - 3 y = 2$ , $7 x - 21 y = 14$ , $3 x - 9 y = 6$

Step 1

Add $3 y$ to both sides of the equation.

$x = 2 + 3 y$

$7 x - 21 y = 14$

$3 x - 9 y = 6$

Step 2

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

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $7 x - 21 y = 14$ with $2 + 3 y$ .

$7 (2 + 3 y) - 21 y = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $7 (2 + 3 y) - 21 y$ .

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.

$7 \cdot 2 + 7 (3 y) - 21 y = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

Step 2.2.1.1.2

Multiply $7$ by $2$ .

$14 + 7 (3 y) - 21 y = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

Step 2.2.1.1.3

Multiply $3$ by $7$ .

$14 + 21 y - 21 y = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

$14 + 21 y - 21 y = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

Step 2.2.1.2

Combine the opposite terms in $14 + 21 y - 21 y$ .

Tap for more steps...

Step 2.2.1.2.1

Subtract $21 y$ from $21 y$ .

$14 + 0 = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

Step 2.2.1.2.2

Add $14$ and $0$ .

$14 = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

$3 x - 9 y = 6$

Step 2.3

Replace all occurrences of $x$ in $3 x - 9 y = 6$ with $2 + 3 y$ .

$3 (2 + 3 y) - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $3 (2 + 3 y) - 9 y$ .

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.

$3 \cdot 2 + 3 (3 y) - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

Step 2.4.1.1.2

Multiply $3$ by $2$ .

$6 + 3 (3 y) - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

Step 2.4.1.1.3

Multiply $3$ by $3$ .

$6 + 9 y - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

$6 + 9 y - 9 y = 6$

$14 = 14$

$x = 2 + 3 y$

Step 2.4.1.2

Combine the opposite terms in $6 + 9 y - 9 y$ .

Tap for more steps...

Step 2.4.1.2.1

Subtract $9 y$ from $9 y$ .

$6 + 0 = 6$

$14 = 14$

$x = 2 + 3 y$

Step 2.4.1.2.2

Add $6$ and $0$ .

$6 = 6$

$14 = 14$

$x = 2 + 3 y$

$6 = 6$

$14 = 14$

$x = 2 + 3 y$

$6 = 6$

$14 = 14$

$x = 2 + 3 y$

$6 = 6$

$14 = 14$

$x = 2 + 3 y$

$6 = 6$

$14 = 14$

$x = 2 + 3 y$

Step 3

Remove any equations from the system that are always true.

$x = 2 + 3 y$

Step 4