Solve the System of Equations -x+6y=2 and -3x+y=-11

$- x + 6 y = 2$ and $- 3 x + y = - 11$

Add $3 x$ to both sides of the equation.

$y = - 11 + 3 x$

$- x + 6 y = 2$

Replace all occurrences of $y$ with $- 11 + 3 x$ in each equation.

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

$- x + 6 (- 11 + 3 x) = 2$

$y = - 11 + 3 x$

Simplify the left side.

Simplify $- x + 6 (- 11 + 3 x)$ .

Simplify each term.

Apply the distributive property.

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

$y = - 11 + 3 x$

Multiply $6$ by $- 11$ .

$- x - 66 + 6 (3 x) = 2$

$y = - 11 + 3 x$

Multiply $3$ by $6$ .

$- x - 66 + 18 x = 2$

$y = - 11 + 3 x$

$- x - 66 + 18 x = 2$

$y = - 11 + 3 x$

Add $- x$ and $18 x$ .

$17 x - 66 = 2$

$y = - 11 + 3 x$

$17 x - 66 = 2$

$y = - 11 + 3 x$

$17 x - 66 = 2$

$y = - 11 + 3 x$

$17 x - 66 = 2$

$y = - 11 + 3 x$

Solve for $x$ in $17 x - 66 = 2$ .

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

Add $66$ to both sides of the equation.

$17 x = 2 + 66$

$y = - 11 + 3 x$

Add $2$ and $66$ .

$17 x = 68$

$y = - 11 + 3 x$

$17 x = 68$

$y = - 11 + 3 x$

Divide each term in $17 x = 68$ by $17$ and simplify.

Divide each term in $17 x = 68$ by $17$ .

$\frac{17 x}{17} = \frac{68}{17}$

$y = - 11 + 3 x$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 x}{17} = \frac{68}{17}$

$y = - 11 + 3 x$

Divide $x$ by $1$ .

$x = \frac{68}{17}$

$y = - 11 + 3 x$

$x = \frac{68}{17}$

$y = - 11 + 3 x$

$x = \frac{68}{17}$

$y = - 11 + 3 x$

Simplify the right side.

Divide $68$ by $17$ .

$x = 4$

$y = - 11 + 3 x$

$x = 4$

$y = - 11 + 3 x$

$x = 4$

$y = - 11 + 3 x$

$x = 4$

$y = - 11 + 3 x$

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

Replace all occurrences of $x$ in $y = - 11 + 3 x$ with $4$ .

$y = - 11 + 3 (4)$

$x = 4$

Simplify the right side.

Simplify $- 11 + 3 (4)$ .

Multiply $3$ by $4$ .

$y = - 11 + 12$

$x = 4$

Add $- 11$ and $12$ .

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

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

$(4, 1)$

The result can be shown in multiple forms.

Point Form:

$(4, 1)$

Equation Form:

$x = 4, y = 1$

Solve the System of Equations -x+6y=2 and -3x+y=-11

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