Precalculus Examples

$x + 2 y = 3$ , $- x - y = - 5$

Step 1

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

$x = 3 - 2 y$

$- x - y = - 5$

Step 2

Replace all occurrences of $x$ with $3 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- x - y = - 5$ with $3 - 2 y$ .

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

$x = 3 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- (3 - 2 y) - y$ .

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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.

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

$x = 3 - 2 y$

Step 2.2.1.1.2

Multiply $- 1$ by $3$ .

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

$x = 3 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $- 1$ .

$- 3 + 2 y - y = - 5$

$x = 3 - 2 y$

$- 3 + 2 y - y = - 5$

$x = 3 - 2 y$

Step 2.2.1.2

Subtract $y$ from $2 y$ .

$- 3 + y = - 5$

$x = 3 - 2 y$

$- 3 + y = - 5$

$x = 3 - 2 y$

$- 3 + y = - 5$

$x = 3 - 2 y$

$- 3 + y = - 5$

$x = 3 - 2 y$

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

$y = - 5 + 3$

$x = 3 - 2 y$

Step 3.2

Add $- 5$ and $3$ .

$y = - 2$

$x = 3 - 2 y$

$y = - 2$

$x = 3 - 2 y$

Step 4

Replace all occurrences of $y$ with $- 2$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 3 - 2 y$ with $- 2$ .

$x = 3 - 2 \cdot - 2$

$y = - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $3 - 2 \cdot - 2$ .

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Step 4.2.1.1

Multiply $- 2$ by $- 2$ .

$x = 3 + 4$

$y = - 2$

Step 4.2.1.2

Add $3$ and $4$ .

$x = 7$

$y = - 2$

$x = 7$

$y = - 2$

$x = 7$

$y = - 2$

$x = 7$

$y = - 2$

Step 5

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

$(7, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, - 2)$

Equation Form:

$x = 7, y = - 2$

Step 7