Algebra Examples

$p - 3 q = - 1$ $- 5 p + 16 q = 5$

Step 1

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

$p = - 1 + 3 q$

$- 5 p + 16 q = 5$

Step 2

Replace all occurrences of $p$ with $- 1 + 3 q$ in each equation.

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Step 2.1

Replace all occurrences of $p$ in $- 5 p + 16 q = 5$ with $- 1 + 3 q$ .

$- 5 (- 1 + 3 q) + 16 q = 5$

$p = - 1 + 3 q$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 5 (- 1 + 3 q) + 16 q$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$- 5 \cdot - 1 - 5 (3 q) + 16 q = 5$

$p = - 1 + 3 q$

Step 2.2.1.1.2

Multiply $- 5$ by $- 1$ .

$5 - 5 (3 q) + 16 q = 5$

$p = - 1 + 3 q$

Step 2.2.1.1.3

Multiply $3$ by $- 5$ .

$5 - 15 q + 16 q = 5$

$p = - 1 + 3 q$

$5 - 15 q + 16 q = 5$

$p = - 1 + 3 q$

Step 2.2.1.2

Add $- 15 q$ and $16 q$ .

$5 + q = 5$

$p = - 1 + 3 q$

$5 + q = 5$

$p = - 1 + 3 q$

$5 + q = 5$

$p = - 1 + 3 q$

$5 + q = 5$

$p = - 1 + 3 q$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

$q = 5 - 5$

$p = - 1 + 3 q$

Step 3.2

Subtract $5$ from $5$ .

$q = 0$

$p = - 1 + 3 q$

$q = 0$

$p = - 1 + 3 q$

Step 4

Replace all occurrences of $q$ with $0$ in each equation.

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Step 4.1

Replace all occurrences of $q$ in $p = - 1 + 3 q$ with $0$ .

$p = - 1 + 3 (0)$

$q = 0$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 1 + 3 (0)$ .

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Step 4.2.1.1

Multiply $3$ by $0$ .

$p = - 1 + 0$

$q = 0$

Step 4.2.1.2

Add $- 1$ and $0$ .

$p = - 1$

$q = 0$

$p = - 1$

$q = 0$

$p = - 1$

$q = 0$

$p = - 1$

$q = 0$

Step 5

List all of the solutions.

$p = - 1, q = 0$