Solve the System of Equations 2d+e=8 d-e=4

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

Step 1

Solve for $d$ in $2 d + e = 8$ .

Subtract $e$ from both sides of the equation.

$2 d = 8 - e$

$d - e = 4$

Divide each term in $2 d = 8 - e$ by $2$ and simplify.

Divide each term in $2 d = 8 - e$ by $2$ .

$\frac{2 d}{2} = \frac{8}{2} + \frac{- e}{2}$

$d - e = 4$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 d}{2} = \frac{8}{2} + \frac{- e}{2}$

$d - e = 4$

Divide $d$ by $1$ .

$d = \frac{8}{2} + \frac{- e}{2}$

$d - e = 4$

$d = \frac{8}{2} + \frac{- e}{2}$

$d - e = 4$

$d = \frac{8}{2} + \frac{- e}{2}$

$d - e = 4$

Simplify the right side.

Simplify each term.

Divide $8$ by $2$ .

$d = 4 + \frac{- e}{2}$

$d - e = 4$

Move the negative in front of the fraction.

$d = 4 - \frac{e}{2}$

$d - e = 4$

$d = 4 - \frac{e}{2}$

$d - e = 4$

$d = 4 - \frac{e}{2}$

$d - e = 4$

$d = 4 - \frac{e}{2}$

$d - e = 4$

$d = 4 - \frac{e}{2}$

$d - e = 4$

Step 2

Replace all occurrences of $d$ with $4 - \frac{e}{2}$ in each equation.

Replace all occurrences of $d$ in $d - e = 4$ with $4 - \frac{e}{2}$ .

$(4 - \frac{e}{2}) - e = 4$

$d = 4 - \frac{e}{2}$

Simplify the left side.

Simplify $(4 - \frac{e}{2}) - e$ .

To write $- e$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 - \frac{e}{2} - e \cdot \frac{2}{2} = 4$

$d = 4 - \frac{e}{2}$

Combine fractions.

Combine $- e$ and $\frac{2}{2}$ .

$4 - \frac{e}{2} + \frac{- e \cdot 2}{2} = 4$

$d = 4 - \frac{e}{2}$

Combine the numerators over the common denominator.

$4 + \frac{- e - e \cdot 2}{2} = 4$

$d = 4 - \frac{e}{2}$

$4 + \frac{- e - e \cdot 2}{2} = 4$

$d = 4 - \frac{e}{2}$

Simplify each term.

Simplify the numerator.

Multiply $2$ by $- 1$ .

$4 + \frac{- e - 2 e}{2} = 4$

$d = 4 - \frac{e}{2}$

Subtract $2 e$ from $- e$ .

$4 + \frac{- 3 e}{2} = 4$

$d = 4 - \frac{e}{2}$

$4 + \frac{- 3 e}{2} = 4$

$d = 4 - \frac{e}{2}$

Move the negative in front of the fraction.

$4 - \frac{3 e}{2} = 4$

$d = 4 - \frac{e}{2}$

$4 - \frac{3 e}{2} = 4$

$d = 4 - \frac{e}{2}$

$4 - \frac{3 e}{2} = 4$

$d = 4 - \frac{e}{2}$

$4 - \frac{3 e}{2} = 4$

$d = 4 - \frac{e}{2}$

$4 - \frac{3 e}{2} = 4$

$d = 4 - \frac{e}{2}$

Step 3

Since $4 - \frac{3 e}{2} = 4$ is not true, there is no solution.

No solution

Solve the System of Equations 2d+e=8 d-e=4

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