Precalculus Examples

$2 x + 10 y + 6 z = - 50$ , $x + 5 y + 3 z = 10$ , $x + y + z = - 5$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $5 y$ from both sides of the equation.

$x + 3 z = 10 - 5 y$

$2 x + 10 y + 6 z = - 50$

$x + y + z = - 5$

Step 1.2

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

$x = 10 - 5 y - 3 z$

$2 x + 10 y + 6 z = - 50$

$x + y + z = - 5$

$x = 10 - 5 y - 3 z$

$2 x + 10 y + 6 z = - 50$

$x + y + z = - 5$

Step 2

Replace all occurrences of $x$ with $10 - 5 y - 3 z$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $x$ in $2 x + 10 y + 6 z = - 50$ with $10 - 5 y - 3 z$ .

$2 (10 - 5 y - 3 z) + 10 y + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $2 (10 - 5 y - 3 z) + 10 y + 6 z$ .

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.

$2 \cdot 10 + 2 (- 5 y) + 2 (- 3 z) + 10 y + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2.1.1.2

Simplify.

Tap for more steps...

Step 2.2.1.1.2.1

Multiply $2$ by $10$ .

$20 + 2 (- 5 y) + 2 (- 3 z) + 10 y + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2.1.1.2.2

Multiply $- 5$ by $2$ .

$20 - 10 y + 2 (- 3 z) + 10 y + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2.1.1.2.3

Multiply $- 3$ by $2$ .

$20 - 10 y - 6 z + 10 y + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

$20 - 10 y - 6 z + 10 y + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

$20 - 10 y - 6 z + 10 y + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2.1.2

Combine the opposite terms in $20 - 10 y - 6 z + 10 y + 6 z$ .

Tap for more steps...

Step 2.2.1.2.1

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

$20 - 6 z + 0 + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2.1.2.2

Add $20 - 6 z$ and $0$ .

$20 - 6 z + 6 z = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2.1.2.3

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

$20 + 0 = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.2.1.2.4

Add $20$ and $0$ .

$20 = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

$x + y + z = - 5$

Step 2.3

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

$(10 - 5 y - 3 z) + y + z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

Step 2.4

Simplify the left side.

Tap for more steps...

Step 2.4.1

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

Tap for more steps...

Step 2.4.1.1

Add $- 5 y$ and $y$ .

$10 - 4 y - 3 z + z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

Step 2.4.1.2

Add $- 3 z$ and $z$ .

$10 - 4 y - 2 z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

$10 - 4 y - 2 z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

$10 - 4 y - 2 z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

$10 - 4 y - 2 z = - 5$

$20 = - 50$

$x = 10 - 5 y - 3 z$

Step 3

Since $20 = - 50$ is not true, there is no solution.

No solution