Solve the System of Equations 6x-7y=37 x+14y=-9

$6 x - 7 y = 37$ $x + 14 y = - 9$

Subtract $14 y$ from both sides of the equation.

$x = - 9 - 14 y$

$6 x - 7 y = 37$

Replace all occurrences of $x$ with $- 9 - 14 y$ in each equation.

Replace all occurrences of $x$ in $6 x - 7 y = 37$ with $- 9 - 14 y$ .

$6 (- 9 - 14 y) - 7 y = 37$

$x = - 9 - 14 y$

Simplify the left side.

Simplify $6 (- 9 - 14 y) - 7 y$ .

Simplify each term.

Apply the distributive property.

$6 \cdot - 9 + 6 (- 14 y) - 7 y = 37$

$x = - 9 - 14 y$

Multiply $6$ by $- 9$ .

$- 54 + 6 (- 14 y) - 7 y = 37$

$x = - 9 - 14 y$

Multiply $- 14$ by $6$ .

$- 54 - 84 y - 7 y = 37$

$x = - 9 - 14 y$

$- 54 - 84 y - 7 y = 37$

$x = - 9 - 14 y$

Subtract $7 y$ from $- 84 y$ .

$- 54 - 91 y = 37$

$x = - 9 - 14 y$

$- 54 - 91 y = 37$

$x = - 9 - 14 y$

$- 54 - 91 y = 37$

$x = - 9 - 14 y$

$- 54 - 91 y = 37$

$x = - 9 - 14 y$

Solve for $y$ in $- 54 - 91 y = 37$ .

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

Add $54$ to both sides of the equation.

$- 91 y = 37 + 54$

$x = - 9 - 14 y$

Add $37$ and $54$ .

$- 91 y = 91$

$x = - 9 - 14 y$

$- 91 y = 91$

$x = - 9 - 14 y$

Divide each term in $- 91 y = 91$ by $- 91$ and simplify.

Divide each term in $- 91 y = 91$ by $- 91$ .

$\frac{- 91 y}{- 91} = \frac{91}{- 91}$

$x = - 9 - 14 y$

Simplify the left side.

Cancel the common factor of $- 91$ .

Cancel the common factor.

$\frac{- 91 y}{- 91} = \frac{91}{- 91}$

$x = - 9 - 14 y$

Divide $y$ by $1$ .

$y = \frac{91}{- 91}$

$x = - 9 - 14 y$

$y = \frac{91}{- 91}$

$x = - 9 - 14 y$

$y = \frac{91}{- 91}$

$x = - 9 - 14 y$

Simplify the right side.

Divide $91$ by $- 91$ .

$y = - 1$

$x = - 9 - 14 y$

$y = - 1$

$x = - 9 - 14 y$

$y = - 1$

$x = - 9 - 14 y$

$y = - 1$

$x = - 9 - 14 y$

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

Replace all occurrences of $y$ in $x = - 9 - 14 y$ with $- 1$ .

$x = - 9 - 14 \cdot - 1$

$y = - 1$

Simplify the right side.

Simplify $- 9 - 14 \cdot - 1$ .

Multiply $- 14$ by $- 1$ .

$x = - 9 + 14$

$y = - 1$

Add $- 9$ and $14$ .

$x = 5$

$y = - 1$

$x = 5$

$y = - 1$

$x = 5$

$y = - 1$

$x = 5$

$y = - 1$

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

$(5, - 1)$

The result can be shown in multiple forms.

Point Form:

$(5, - 1)$

Equation Form:

$x = 5, y = - 1$

Solve the System of Equations 6x-7y=37 x+14y=-9

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