Solve the System of Equations 2x-y=8 8x-4y=8

$2 x - y = 8$ $8 x - 4 y = 8$

Step 1

Solve for $x$ in $2 x - y = 8$ .

Add $y$ to both sides of the equation.

$2 x = 8 + y$

$8 x - 4 y = 8$

Divide each term in $2 x = 8 + y$ by $2$ and simplify.

Divide each term in $2 x = 8 + y$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2} + \frac{y}{2}$

$8 x - 4 y = 8$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2} + \frac{y}{2}$

$8 x - 4 y = 8$

Divide $x$ by $1$ .

$x = \frac{8}{2} + \frac{y}{2}$

$8 x - 4 y = 8$

$x = \frac{8}{2} + \frac{y}{2}$

$8 x - 4 y = 8$

$x = \frac{8}{2} + \frac{y}{2}$

$8 x - 4 y = 8$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4 + \frac{y}{2}$

$8 x - 4 y = 8$

$x = 4 + \frac{y}{2}$

$8 x - 4 y = 8$

$x = 4 + \frac{y}{2}$

$8 x - 4 y = 8$

$x = 4 + \frac{y}{2}$

$8 x - 4 y = 8$

Step 2

Replace all occurrences of $x$ with $4 + \frac{y}{2}$ in each equation.

Replace all occurrences of $x$ in $8 x - 4 y = 8$ with $4 + \frac{y}{2}$ .

$8 (4 + \frac{y}{2}) - 4 y = 8$

$x = 4 + \frac{y}{2}$

Simplify the left side.

Simplify $8 (4 + \frac{y}{2}) - 4 y$ .

Simplify each term.

Apply the distributive property.

$8 \cdot 4 + 8 (\frac{y}{2}) - 4 y = 8$

$x = 4 + \frac{y}{2}$

Multiply $8$ by $4$ .

$32 + 8 (\frac{y}{2}) - 4 y = 8$

$x = 4 + \frac{y}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$32 + 2 (4) (\frac{y}{2}) - 4 y = 8$

$x = 4 + \frac{y}{2}$

Cancel the common factor.

$32 + 2 \cdot (4 (\frac{y}{2})) - 4 y = 8$

$x = 4 + \frac{y}{2}$

Rewrite the expression.

$32 + 4 y - 4 y = 8$

$x = 4 + \frac{y}{2}$

$32 + 4 y - 4 y = 8$

$x = 4 + \frac{y}{2}$

$32 + 4 y - 4 y = 8$

$x = 4 + \frac{y}{2}$

Combine the opposite terms in $32 + 4 y - 4 y$ .

Subtract $4 y$ from $4 y$ .

$32 + 0 = 8$

$x = 4 + \frac{y}{2}$

Add $32$ and $0$ .

$32 = 8$

$x = 4 + \frac{y}{2}$

$32 = 8$

$x = 4 + \frac{y}{2}$

$32 = 8$

$x = 4 + \frac{y}{2}$

$32 = 8$

$x = 4 + \frac{y}{2}$

$32 = 8$

$x = 4 + \frac{y}{2}$

Step 3

Since $32 = 8$ is not true, there is no solution.

No solution

Step 4

Solve the System of Equations 2x-y=8 8x-4y=8

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