Algebra Examples

$3 x - 5 y + z = 5$ , $x + y = 7$

Step 1

Solve the equation for $z$ .

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Step 1.1

Simplify $3 x - 5 (7 - x) + z$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$3 x - 5 \cdot 7 - 5 (- x) + z = 5$

$y = 7 - x$

Step 1.1.1.2

Multiply $- 5$ by $7$ .

$3 x - 35 - 5 (- x) + z = 5$

$y = 7 - x$

Step 1.1.1.3

Multiply $- 1$ by $- 5$ .

$3 x - 35 + 5 x + z = 5$

$y = 7 - x$

$3 x - 35 + 5 x + z = 5$

$y = 7 - x$

Step 1.1.2

Add $3 x$ and $5 x$ .

$8 x - 35 + z = 5$

$y = 7 - x$

$8 x - 35 + z = 5$

$y = 7 - x$

Step 1.2

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

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Step 1.2.1

Subtract $8 x$ from both sides of the equation.

$- 35 + z = 5 - 8 x$

$y = 7 - x$

Step 1.2.2

Add $35$ to both sides of the equation.

$z = 5 - 8 x + 35$

$y = 7 - x$

Step 1.2.3

Add $5$ and $35$ .

$z = - 8 x + 40$

$y = 7 - x$

$z = - 8 x + 40$

$y = 7 - x$

$z = - 8 x + 40$

$y = 7 - x$

Step 2

Simplify the right side.

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Step 2.1

Reorder $7$ and $- x$ .

$y = - x + 7$

$z = - 8 x + 40$

$y = - x + 7$

$z = - 8 x + 40$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$