Algebra Examples

$3 x + y = - 8$ $- 2 x - y = 6$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = - 8 - 3 x$

$- 2 x - y = 6$

Step 2

Replace all occurrences of $y$ with $- 8 - 3 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 2 x - y = 6$ with $- 8 - 3 x$ .

$- 2 x - (- 8 - 3 x) = 6$

$y = - 8 - 3 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 2 x - (- 8 - 3 x)$ .

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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.

$- 2 x + 8 - (- 3 x) = 6$

$y = - 8 - 3 x$

Step 2.2.1.1.2

Multiply $- 1$ by $- 8$ .

$- 2 x + 8 - (- 3 x) = 6$

$y = - 8 - 3 x$

Step 2.2.1.1.3

Multiply $- 3$ by $- 1$ .

$- 2 x + 8 + 3 x = 6$

$y = - 8 - 3 x$

$- 2 x + 8 + 3 x = 6$

$y = - 8 - 3 x$

Step 2.2.1.2

Add $- 2 x$ and $3 x$ .

$x + 8 = 6$

$y = - 8 - 3 x$

$x + 8 = 6$

$y = - 8 - 3 x$

$x + 8 = 6$

$y = - 8 - 3 x$

$x + 8 = 6$

$y = - 8 - 3 x$

Step 3

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

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Step 3.1

Subtract $8$ from both sides of the equation.

$x = 6 - 8$

$y = - 8 - 3 x$

Step 3.2

Subtract $8$ from $6$ .

$x = - 2$

$y = - 8 - 3 x$

$x = - 2$

$y = - 8 - 3 x$

Step 4

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

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Step 4.1

Replace all occurrences of $x$ in $y = - 8 - 3 x$ with $- 2$ .

$y = - 8 - 3 \cdot - 2$

$x = - 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 8 - 3 \cdot - 2$ .

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Step 4.2.1.1

Multiply $- 3$ by $- 2$ .

$y = - 8 + 6$

$x = - 2$

Step 4.2.1.2

Add $- 8$ and $6$ .

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

$y = - 2$

$x = - 2$

Step 5

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

$(- 2, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, - 2)$

Equation Form:

$x = - 2, y = - 2$

Step 7