Algebra Examples

$5 x + 10 y + 15 z = 60$ $2 x + 4 y + 6 z = 60$ $x + 2 y + 3 z = 60$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $2 y$ from both sides of the equation.

$x + 3 z = 60 - 2 y$

$5 x + 10 y + 15 z = 60$

$2 x + 4 y + 6 z = 60$

Step 1.2

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

$x = 60 - 2 y - 3 z$

$5 x + 10 y + 15 z = 60$

$2 x + 4 y + 6 z = 60$

$x = 60 - 2 y - 3 z$

$5 x + 10 y + 15 z = 60$

$2 x + 4 y + 6 z = 60$

Step 2

Replace all occurrences of $x$ with $60 - 2 y - 3 z$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $5 x + 10 y + 15 z = 60$ with $60 - 2 y - 3 z$ .

$5 (60 - 2 y - 3 z) + 10 y + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $5 (60 - 2 y - 3 z) + 10 y + 15 z$ .

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.

$5 \cdot 60 + 5 (- 2 y) + 5 (- 3 z) + 10 y + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Multiply $5$ by $60$ .

$300 + 5 (- 2 y) + 5 (- 3 z) + 10 y + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2.1.1.2.2

Multiply $- 2$ by $5$ .

$300 - 10 y + 5 (- 3 z) + 10 y + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2.1.1.2.3

Multiply $- 3$ by $5$ .

$300 - 10 y - 15 z + 10 y + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

$300 - 10 y - 15 z + 10 y + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

$300 - 10 y - 15 z + 10 y + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2.1.2

Combine the opposite terms in $300 - 10 y - 15 z + 10 y + 15 z$ .

Tap for more steps...

Step 2.2.1.2.1

Add $- 10 y$ and $10 y$ .

$300 - 15 z + 0 + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2.1.2.2

Add $300 - 15 z$ and $0$ .

$300 - 15 z + 15 z = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2.1.2.3

Add $- 15 z$ and $15 z$ .

$300 + 0 = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.2.1.2.4

Add $300$ and $0$ .

$300 = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$2 x + 4 y + 6 z = 60$

Step 2.3

Replace all occurrences of $x$ in $2 x + 4 y + 6 z = 60$ with $60 - 2 y - 3 z$ .

$2 (60 - 2 y - 3 z) + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

Simplify $2 (60 - 2 y - 3 z) + 4 y + 6 z$ .

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.

$2 \cdot 60 + 2 (- 2 y) + 2 (- 3 z) + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4.1.1.2

Simplify.

Tap for more steps...

Step 2.4.1.1.2.1

Multiply $2$ by $60$ .

$120 + 2 (- 2 y) + 2 (- 3 z) + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4.1.1.2.2

Multiply $- 2$ by $2$ .

$120 - 4 y + 2 (- 3 z) + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4.1.1.2.3

Multiply $- 3$ by $2$ .

$120 - 4 y - 6 z + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$120 - 4 y - 6 z + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$120 - 4 y - 6 z + 4 y + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4.1.2

Combine the opposite terms in $120 - 4 y - 6 z + 4 y + 6 z$ .

Tap for more steps...

Step 2.4.1.2.1

Add $- 4 y$ and $4 y$ .

$120 - 6 z + 0 + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4.1.2.2

Add $120 - 6 z$ and $0$ .

$120 - 6 z + 6 z = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4.1.2.3

Add $- 6 z$ and $6 z$ .

$120 + 0 = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 2.4.1.2.4

Add $120$ and $0$ .

$120 = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$120 = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$120 = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$120 = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

$120 = 60$

$300 = 60$

$x = 60 - 2 y - 3 z$

Step 3

Since $120 = 60$ is not true, there is no solution.

No solution