Algebra Examples

$2 d + e = 8$ $d - e = 4$

Step 1

Move all terms containing variables to the left.

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Step 1.1

Subtract $e$ from both sides of the equation.

$2 d = 8 - e, d - e = 4$

Step 1.2

Add $e$ to both sides of the equation.

$2 d = 8 - e, d = 4 + e$

Step 2

Multiply each equation by the value that makes the coefficients of $d$ opposite.

$2 d = 8 - e$

$(- 2) \cdot (d) = (- 2) (4 + e)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Multiply $- 2$ by $d$ .

$2 d = 8 - e$

$- 2 d = (- 2) (4 + e)$

$2 d = 8 - e$

$- 2 d = (- 2) (4 + e)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(- 2) (4 + e)$ .

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Step 3.2.1.1

Apply the distributive property.

$2 d = 8 - e$

$- 2 d = - 2 \cdot 4 - 2 e$

Step 3.2.1.2

Multiply $- 2$ by $4$ .

$2 d = 8 - e$

$- 2 d = - 8 - 2 e$

$2 d = 8 - e$

$- 2 d = - 8 - 2 e$

$2 d = 8 - e$

$- 2 d = - 8 - 2 e$

$2 d = 8 - e$

$- 2 d = - 8 - 2 e$

Step 4

Add the two equations together to eliminate $d$ from the system.

		$2$	$d$	$=$		$8$		$-$	$e$
$+$	$-$	$2$	$d$	$=$	$-$	$8$	$-$	$2$	$e$
			$0$	$=$			$-$	$3$	$e$

Step 5

Rewrite the equation as $- 3 e = 0$ .

$- 3 e = 0$

Step 6

Multiply $- 3$ by $2.71828182$ .

$- 8.15484548 = 0$

Step 7

Since $- 8.15484548 \neq 0$ , there are no solutions.

No solution

		$2$	$d$	$=$		$8$		$-$	$e$
$+$	$-$	$2$	$d$	$=$	$-$	$8$	$-$	$2$	$e$
			$0$	$=$			$-$	$3$	$e$

		$2$	$d$	$=$		$8$		$-$	$e$
$+$	$-$	$2$	$d$	$=$	$-$	$8$	$-$	$2$	$e$
			$0$	$=$			$-$	$3$	$e$

		$2$	$d$	$=$		$8$		$-$	$e$
$+$	$-$	$2$	$d$	$=$	$-$	$8$	$-$	$2$	$e$
			$0$	$=$			$-$	$3$	$e$