Solve by Substitution 2x+8y=6 , -5x-20y=-15

$2 x + 8 y = 6$ , $- 5 x - 20 y = - 15$

Step 1

Solve for $x$ in $2 x + 8 y = 6$ .

Subtract $8 y$ from both sides of the equation.

$2 x = 6 - 8 y$

$- 5 x - 20 y = - 15$

Divide each term in $2 x = 6 - 8 y$ by $2$ and simplify.

Divide each term in $2 x = 6 - 8 y$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2} + \frac{- 8 y}{2}$

$- 5 x - 20 y = - 15$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2} + \frac{- 8 y}{2}$

$- 5 x - 20 y = - 15$

Divide $x$ by $1$ .

$x = \frac{6}{2} + \frac{- 8 y}{2}$

$- 5 x - 20 y = - 15$

$x = \frac{6}{2} + \frac{- 8 y}{2}$

$- 5 x - 20 y = - 15$

$x = \frac{6}{2} + \frac{- 8 y}{2}$

$- 5 x - 20 y = - 15$

Simplify the right side.

Simplify each term.

Divide $6$ by $2$ .

$x = 3 + \frac{- 8 y}{2}$

$- 5 x - 20 y = - 15$

Cancel the common factor of $- 8$ and $2$ .

Factor $2$ out of $- 8 y$ .

$x = 3 + \frac{2 (- 4 y)}{2}$

$- 5 x - 20 y = - 15$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = 3 + \frac{2 (- 4 y)}{2 (1)}$

$- 5 x - 20 y = - 15$

Cancel the common factor.

$x = 3 + \frac{2 (- 4 y)}{2 \cdot 1}$

$- 5 x - 20 y = - 15$

Rewrite the expression.

$x = 3 + \frac{- 4 y}{1}$

$- 5 x - 20 y = - 15$

Divide $- 4 y$ by $1$ .

$x = 3 - 4 y$

$- 5 x - 20 y = - 15$

$x = 3 - 4 y$

$- 5 x - 20 y = - 15$

$x = 3 - 4 y$

$- 5 x - 20 y = - 15$

$x = 3 - 4 y$

$- 5 x - 20 y = - 15$

$x = 3 - 4 y$

$- 5 x - 20 y = - 15$

$x = 3 - 4 y$

$- 5 x - 20 y = - 15$

$x = 3 - 4 y$

$- 5 x - 20 y = - 15$

Step 2

Replace all occurrences of $x$ with $3 - 4 y$ in each equation.

Replace all occurrences of $x$ in $- 5 x - 20 y = - 15$ with $3 - 4 y$ .

$- 5 (3 - 4 y) - 20 y = - 15$

$x = 3 - 4 y$

Simplify the left side.

Simplify $- 5 (3 - 4 y) - 20 y$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot 3 - 5 (- 4 y) - 20 y = - 15$

$x = 3 - 4 y$

Multiply $- 5$ by $3$ .

$- 15 - 5 (- 4 y) - 20 y = - 15$

$x = 3 - 4 y$

Multiply $- 4$ by $- 5$ .

$- 15 + 20 y - 20 y = - 15$

$x = 3 - 4 y$

$- 15 + 20 y - 20 y = - 15$

$x = 3 - 4 y$

Combine the opposite terms in $- 15 + 20 y - 20 y$ .

Subtract $20 y$ from $20 y$ .

$- 15 + 0 = - 15$

$x = 3 - 4 y$

Add $- 15$ and $0$ .

$- 15 = - 15$

$x = 3 - 4 y$

$- 15 = - 15$

$x = 3 - 4 y$

$- 15 = - 15$

$x = 3 - 4 y$

$- 15 = - 15$

$x = 3 - 4 y$

$- 15 = - 15$

$x = 3 - 4 y$

Step 3

Remove any equations from the system that are always true.

$x = 3 - 4 y$

Step 4

Solve by Substitution 2x+8y=6 , -5x-20y=-15

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