Algebra Examples

$x + y = 5$ $y + 1 = 3 x^{2} + 2 x$

Step 1

Subtract $y$ from both sides of the equation.

$x = 5 - y$

$y + 1 = 3 x^{2} + 2 x$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $y + 1 = 3 x^{2} + 2 x$ with $5 - y$ .

$y + 1 = 3 {(5 - y)}^{2} + 2 (5 - y)$

$x = 5 - y$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $3 {(5 - y)}^{2} + 2 (5 - y)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Rewrite ${(5 - y)}^{2}$ as $(5 - y) (5 - y)$ .

$y + 1 = 3 ((5 - y) (5 - y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.2

Expand $(5 - y) (5 - y)$ using the FOIL Method.

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Step 2.2.1.1.2.1

Apply the distributive property.

$y + 1 = 3 (5 (5 - y) - y (5 - y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.2.2

Apply the distributive property.

$y + 1 = 3 (5 \cdot 5 + 5 (- y) - y (5 - y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.2.3

Apply the distributive property.

$y + 1 = 3 (5 \cdot 5 + 5 (- y) - y \cdot 5 - y (- y)) + 2 (5 - y)$

$x = 5 - y$

$y + 1 = 3 (5 \cdot 5 + 5 (- y) - y \cdot 5 - y (- y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3

Simplify and combine like terms.

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Step 2.2.1.1.3.1

Simplify each term.

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Step 2.2.1.1.3.1.1

Multiply $5$ by $5$ .

$y + 1 = 3 (25 + 5 (- y) - y \cdot 5 - y (- y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.1.2

Multiply $- 1$ by $5$ .

$y + 1 = 3 (25 - 5 y - y \cdot 5 - y (- y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.1.3

Multiply $5$ by $- 1$ .

$y + 1 = 3 (25 - 5 y - 5 y - y (- y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.1.4

Rewrite using the commutative property of multiplication.

$y + 1 = 3 (25 - 5 y - 5 y - 1 \cdot (- 1 y \cdot y)) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.1.5

Multiply $y$ by $y$ by adding the exponents.

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Step 2.2.1.1.3.1.5.1

Move $y$ .

$y + 1 = 3 (25 - 5 y - 5 y - 1 \cdot (- 1 (y \cdot y))) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.1.5.2

Multiply $y$ by $y$ .

$y + 1 = 3 (25 - 5 y - 5 y - 1 \cdot (- 1 y^{2})) + 2 (5 - y)$

$x = 5 - y$

$y + 1 = 3 (25 - 5 y - 5 y - 1 \cdot (- 1 y^{2})) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.1.6

Multiply $- 1$ by $- 1$ .

$y + 1 = 3 (25 - 5 y - 5 y + 1 y^{2}) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.1.7

Multiply $y^{2}$ by $1$ .

$y + 1 = 3 (25 - 5 y - 5 y + y^{2}) + 2 (5 - y)$

$x = 5 - y$

$y + 1 = 3 (25 - 5 y - 5 y + y^{2}) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.3.2

Subtract $5 y$ from $- 5 y$ .

$y + 1 = 3 (25 - 10 y + y^{2}) + 2 (5 - y)$

$x = 5 - y$

$y + 1 = 3 (25 - 10 y + y^{2}) + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.4

Apply the distributive property.

$y + 1 = 3 \cdot 25 + 3 (- 10 y) + 3 y^{2} + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.5

Simplify.

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Step 2.2.1.1.5.1

Multiply $3$ by $25$ .

$y + 1 = 75 + 3 (- 10 y) + 3 y^{2} + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.5.2

Multiply $- 10$ by $3$ .

$y + 1 = 75 - 30 y + 3 y^{2} + 2 (5 - y)$

$x = 5 - y$

$y + 1 = 75 - 30 y + 3 y^{2} + 2 (5 - y)$

$x = 5 - y$

Step 2.2.1.1.6

Apply the distributive property.

$y + 1 = 75 - 30 y + 3 y^{2} + 2 \cdot 5 + 2 (- y)$

$x = 5 - y$

Step 2.2.1.1.7

Multiply $2$ by $5$ .

$y + 1 = 75 - 30 y + 3 y^{2} + 10 + 2 (- y)$

$x = 5 - y$

Step 2.2.1.1.8

Multiply $- 1$ by $2$ .

$y + 1 = 75 - 30 y + 3 y^{2} + 10 - 2 y$

$x = 5 - y$

$y + 1 = 75 - 30 y + 3 y^{2} + 10 - 2 y$

$x = 5 - y$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $75$ and $10$ .

$y + 1 = - 30 y + 3 y^{2} + 85 - 2 y$

$x = 5 - y$

Step 2.2.1.2.2

Subtract $2 y$ from $- 30 y$ .