Solve the System of Equations -6x+5y=1 6x+4y=-10

$- 6 x + 5 y = 1$ $6 x + 4 y = - 10$

Step 1

Solve for $x$ in $- 6 x + 5 y = 1$ .

Subtract $5 y$ from both sides of the equation.

$- 6 x = 1 - 5 y$

$6 x + 4 y = - 10$

Divide each term in $- 6 x = 1 - 5 y$ by $- 6$ and simplify.

Divide each term in $- 6 x = 1 - 5 y$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{1}{- 6} + \frac{- 5 y}{- 6}$

$6 x + 4 y = - 10$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{1}{- 6} + \frac{- 5 y}{- 6}$

$6 x + 4 y = - 10$

Divide $x$ by $1$ .

$x = \frac{1}{- 6} + \frac{- 5 y}{- 6}$

$6 x + 4 y = - 10$

$x = \frac{1}{- 6} + \frac{- 5 y}{- 6}$

$6 x + 4 y = - 10$

$x = \frac{1}{- 6} + \frac{- 5 y}{- 6}$

$6 x + 4 y = - 10$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{1}{6} + \frac{- 5 y}{- 6}$

$6 x + 4 y = - 10$

Dividing two negative values results in a positive value.

$x = - \frac{1}{6} + \frac{5 y}{6}$

$6 x + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$6 x + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$6 x + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$6 x + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$6 x + 4 y = - 10$

Step 2

Replace all occurrences of $x$ with $- \frac{1}{6} + \frac{5 y}{6}$ in each equation.

Replace all occurrences of $x$ in $6 x + 4 y = - 10$ with $- \frac{1}{6} + \frac{5 y}{6}$ .

$6 (- \frac{1}{6} + \frac{5 y}{6}) + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Simplify the left side.

Simplify $6 (- \frac{1}{6} + \frac{5 y}{6}) + 4 y$ .

Simplify each term.

Apply the distributive property.

$6 (- \frac{1}{6}) + 6 (\frac{5 y}{6}) + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$6 (\frac{- 1}{6}) + 6 (\frac{5 y}{6}) + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Cancel the common factor.

$6 (\frac{- 1}{6}) + 6 (\frac{5 y}{6}) + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Rewrite the expression.

$- 1 + 6 (\frac{5 y}{6}) + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$- 1 + 6 (\frac{5 y}{6}) + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Cancel the common factor of $6$ .

Cancel the common factor.

$- 1 + 6 (\frac{5 y}{6}) + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Rewrite the expression.

$- 1 + 5 y + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$- 1 + 5 y + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$- 1 + 5 y + 4 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Add $5 y$ and $4 y$ .

$- 1 + 9 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$- 1 + 9 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$- 1 + 9 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$- 1 + 9 y = - 10$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Step 3

Solve for $y$ in $- 1 + 9 y = - 10$ .

Move all terms not containing $y$ to the right side of the equation.

Add $1$ to both sides of the equation.

$9 y = - 10 + 1$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Add $- 10$ and $1$ .

$9 y = - 9$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$9 y = - 9$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Divide each term in $9 y = - 9$ by $9$ and simplify.

Divide each term in $9 y = - 9$ by $9$ .

$\frac{9 y}{9} = \frac{- 9}{9}$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 9}{9}$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Divide $y$ by $1$ .

$y = \frac{- 9}{9}$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$y = \frac{- 9}{9}$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$y = \frac{- 9}{9}$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Simplify the right side.

Divide $- 9$ by $9$ .

$y = - 1$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$y = - 1$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$y = - 1$

$x = - \frac{1}{6} + \frac{5 y}{6}$

$y = - 1$

$x = - \frac{1}{6} + \frac{5 y}{6}$

Step 4

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{1}{6} + \frac{5 y}{6}$ with $- 1$ .

$x = - \frac{1}{6} + \frac{5 (- 1)}{6}$

$y = - 1$

Simplify the right side.

Simplify $- \frac{1}{6} + \frac{5 (- 1)}{6}$ .

Combine the numerators over the common denominator.

$x = \frac{- 1 + 5 (- 1)}{6}$

$y = - 1$

Simplify the expression.

Multiply $5$ by $- 1$ .

$x = \frac{- 1 - 5}{6}$

$y = - 1$

Subtract $5$ from $- 1$ .

$x = \frac{- 6}{6}$

$y = - 1$

Divide $- 6$ by $6$ .

$x = - 1$

$y = - 1$

$x = - 1$

$y = - 1$

$x = - 1$

$y = - 1$

$x = - 1$

$y = - 1$

$x = - 1$

$y = - 1$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 1, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, - 1)$

Equation Form:

$x = - 1, y = - 1$

Step 7

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