Algebra Examples

$x - y = 12$ $27 + 3 y = 2 x$

Step 1

Add $y$ to both sides of the equation.

$x = 12 + y$

$27 + 3 y = 2 x$

Step 2

Replace all occurrences of $x$ with $12 + y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $27 + 3 y = 2 x$ with $12 + y$ .

$27 + 3 y = 2 (12 + y)$

$x = 12 + y$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $2 (12 + y)$ .

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Step 2.2.1.1

Apply the distributive property.

$27 + 3 y = 2 \cdot 12 + 2 y$

$x = 12 + y$

Step 2.2.1.2

Multiply $2$ by $12$ .

$27 + 3 y = 24 + 2 y$

$x = 12 + y$

$27 + 3 y = 24 + 2 y$

$x = 12 + y$

$27 + 3 y = 24 + 2 y$

$x = 12 + y$

$27 + 3 y = 24 + 2 y$

$x = 12 + y$

Step 3

Solve for $y$ in $27 + 3 y = 24 + 2 y$ .

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Step 3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.1.1

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

$27 + 3 y - 2 y = 24$

$x = 12 + y$

Step 3.1.2

Subtract $2 y$ from $3 y$ .

$27 + y = 24$

$x = 12 + y$

$27 + y = 24$

$x = 12 + y$

Step 3.2

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

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Step 3.2.1

Subtract $27$ from both sides of the equation.

$y = 24 - 27$

$x = 12 + y$

Step 3.2.2

Subtract $27$ from $24$ .

$y = - 3$

$x = 12 + y$

$y = - 3$

$x = 12 + y$

$y = - 3$

$x = 12 + y$

Step 4

Replace all occurrences of $y$ with $- 3$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 12 + y$ with $- 3$ .

$x = 12 - 3$

$y = - 3$

Step 4.2

Simplify $x = 12 - 3$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = 12 - 3$

$y = - 3$

$x = 12 - 3$

$y = - 3$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Subtract $3$ from $12$ .

$x = 9$

$y = - 3$

$x = 9$

$y = - 3$

$x = 9$

$y = - 3$

$x = 9$

$y = - 3$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(9, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, - 3)$

Equation Form:

$x = 9, y = - 3$

Step 7