Algebra Examples

$x = 7 - y$ $x = - 2 y + 12$

Step 1

Eliminate the equal sides of each equation and combine.

$7 - y = - 2 y + 12$

Step 2

Solve $7 - y = - 2 y + 12$ for $y$ .

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Step 2.1

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

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Step 2.1.1

Add $2 y$ to both sides of the equation.

$7 - y + 2 y = 12$

Step 2.1.2

Add $- y$ and $2 y$ .

$7 + y = 12$

Step 2.2

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

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Step 2.2.1

Subtract $7$ from both sides of the equation.

$y = 12 - 7$

Step 2.2.2

Subtract $7$ from $12$ .

$y = 5$

Step 3

Evaluate $x$ when $y = 5$ .

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Step 3.1

Substitute $5$ for $y$ .

$x = - 2 \cdot 5 + 12$

Step 3.2

Substitute $5$ for $y$ in $x = - 2 \cdot 5 + 12$ and solve for $x$ .

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Step 3.2.1

Remove parentheses.

$x = - 2 \cdot 5 + 12$

Step 3.2.2

Simplify $- 2 \cdot 5 + 12$ .

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Step 3.2.2.1

Multiply $- 2$ by $5$ .

$x = - 10 + 12$

Step 3.2.2.2

Add $- 10$ and $12$ .

$x = 2$

Step 4

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

$(2, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

Step 6