Solve by Substitution -x+2y=10 , -3x+6y=11

$- x + 2 y = 10$ , $- 3 x + 6 y = 11$

Step 1

Solve for $x$ in $- x + 2 y = 10$ .

Subtract $2 y$ from both sides of the equation.

$- x = 10 - 2 y$

$- 3 x + 6 y = 11$

Divide each term in $- x = 10 - 2 y$ by $- 1$ and simplify.

Divide each term in $- x = 10 - 2 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{10}{- 1} + \frac{- 2 y}{- 1}$

$- 3 x + 6 y = 11$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{10}{- 1} + \frac{- 2 y}{- 1}$

$- 3 x + 6 y = 11$

Divide $x$ by $1$ .

$x = \frac{10}{- 1} + \frac{- 2 y}{- 1}$

$- 3 x + 6 y = 11$

$x = \frac{10}{- 1} + \frac{- 2 y}{- 1}$

$- 3 x + 6 y = 11$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 1$ .

$x = - 10 + \frac{- 2 y}{- 1}$

$- 3 x + 6 y = 11$

Move the negative one from the denominator of $\frac{- 2 y}{- 1}$ .

$x = - 10 - 1 \cdot (- 2 y)$

$- 3 x + 6 y = 11$

Rewrite $- 1 \cdot (- 2 y)$ as $- (- 2 y)$ .

$x = - 10 - (- 2 y)$

$- 3 x + 6 y = 11$

Multiply $- 2$ by $- 1$ .

$x = - 10 + 2 y$

$- 3 x + 6 y = 11$

$x = - 10 + 2 y$

$- 3 x + 6 y = 11$

$x = - 10 + 2 y$

$- 3 x + 6 y = 11$

$x = - 10 + 2 y$

$- 3 x + 6 y = 11$

$x = - 10 + 2 y$

$- 3 x + 6 y = 11$

Step 2

Replace all occurrences of $x$ with $- 10 + 2 y$ in each equation.

Replace all occurrences of $x$ in $- 3 x + 6 y = 11$ with $- 10 + 2 y$ .

$- 3 (- 10 + 2 y) + 6 y = 11$

$x = - 10 + 2 y$

Simplify the left side.

Simplify $- 3 (- 10 + 2 y) + 6 y$ .

Simplify each term.

Apply the distributive property.

$- 3 \cdot - 10 - 3 (2 y) + 6 y = 11$

$x = - 10 + 2 y$

Multiply $- 3$ by $- 10$ .

$30 - 3 (2 y) + 6 y = 11$

$x = - 10 + 2 y$

Multiply $2$ by $- 3$ .

$30 - 6 y + 6 y = 11$

$x = - 10 + 2 y$

$30 - 6 y + 6 y = 11$

$x = - 10 + 2 y$

Combine the opposite terms in $30 - 6 y + 6 y$ .

Add $- 6 y$ and $6 y$ .

$30 + 0 = 11$

$x = - 10 + 2 y$

Add $30$ and $0$ .

$30 = 11$

$x = - 10 + 2 y$

$30 = 11$

$x = - 10 + 2 y$

$30 = 11$

$x = - 10 + 2 y$

$30 = 11$

$x = - 10 + 2 y$

$30 = 11$

$x = - 10 + 2 y$

Step 3

Since $30 = 11$ is not true, there is no solution.

No solution

Step 4

Solve by Substitution -x+2y=10 , -3x+6y=11

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