Algebra Examples

$- 8 x - 7 y = 61$ and $x + y = - 8$

Step 1

Subtract $y$ from both sides of the equation.

$x = - 8 - y$

$- 8 x - 7 y = 61$

Step 2

Replace all occurrences of $x$ with $- 8 - y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 8 x - 7 y = 61$ with $- 8 - y$ .

$- 8 (- 8 - y) - 7 y = 61$

$x = - 8 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 8 (- 8 - y) - 7 y$ .

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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.

$- 8 \cdot - 8 - 8 (- y) - 7 y = 61$

$x = - 8 - y$

Step 2.2.1.1.2

Multiply $- 8$ by $- 8$ .

$64 - 8 (- y) - 7 y = 61$

$x = - 8 - y$

Step 2.2.1.1.3

Multiply $- 1$ by $- 8$ .

$64 + 8 y - 7 y = 61$

$x = - 8 - y$

$64 + 8 y - 7 y = 61$

$x = - 8 - y$

Step 2.2.1.2

Subtract $7 y$ from $8 y$ .

$64 + y = 61$

$x = - 8 - y$

$64 + y = 61$

$x = - 8 - y$

$64 + y = 61$

$x = - 8 - y$

$64 + y = 61$

$x = - 8 - y$

Step 3

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

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Step 3.1

Subtract $64$ from both sides of the equation.

$y = 61 - 64$

$x = - 8 - y$

Step 3.2

Subtract $64$ from $61$ .

$y = - 3$

$x = - 8 - y$

$y = - 3$

$x = - 8 - y$

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 $x = - 8 - y$ with $- 3$ .

$x = - 8 - (- 3)$

$y = - 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 8 - (- 3)$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 3$ .

$x = - 8 + 3$

$y = - 3$

Step 4.2.1.2

Add $- 8$ and $3$ .

$x = - 5$

$y = - 3$

$x = - 5$

$y = - 3$

$x = - 5$

$y = - 3$

$x = - 5$

$y = - 3$

Step 5

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

$(- 5, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 5, - 3)$

Equation Form:

$x = - 5, y = - 3$

Step 7