Solve the System of Equations x-y=-3 -8x+y=45

$x - y = - 3$ $- 8 x + y = 45$

Add $y$ to both sides of the equation.

$x = - 3 + y$

$- 8 x + y = 45$

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

Replace all occurrences of $x$ in $- 8 x + y = 45$ with $- 3 + y$ .

$- 8 (- 3 + y) + y = 45$

$x = - 3 + y$

Simplify the left side.

Simplify $- 8 (- 3 + y) + y$ .

Simplify each term.

Apply the distributive property.

$- 8 \cdot - 3 - 8 y + y = 45$

$x = - 3 + y$

Multiply $- 8$ by $- 3$ .

$24 - 8 y + y = 45$

$x = - 3 + y$

$24 - 8 y + y = 45$

$x = - 3 + y$

Add $- 8 y$ and $y$ .

$24 - 7 y = 45$

$x = - 3 + y$

$24 - 7 y = 45$

$x = - 3 + y$

$24 - 7 y = 45$

$x = - 3 + y$

$24 - 7 y = 45$

$x = - 3 + y$

Solve for $y$ in $24 - 7 y = 45$ .

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

Subtract $24$ from both sides of the equation.

$- 7 y = 45 - 24$

$x = - 3 + y$

Subtract $24$ from $45$ .

$- 7 y = 21$

$x = - 3 + y$

$- 7 y = 21$

$x = - 3 + y$

Divide each term in $- 7 y = 21$ by $- 7$ and simplify.

Divide each term in $- 7 y = 21$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{21}{- 7}$

$x = - 3 + y$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{21}{- 7}$

$x = - 3 + y$

Divide $y$ by $1$ .

$y = \frac{21}{- 7}$

$x = - 3 + y$

$y = \frac{21}{- 7}$

$x = - 3 + y$

$y = \frac{21}{- 7}$

$x = - 3 + y$

Simplify the right side.

Divide $21$ by $- 7$ .

$y = - 3$

$x = - 3 + y$

$y = - 3$

$x = - 3 + y$

$y = - 3$

$x = - 3 + y$

$y = - 3$

$x = - 3 + y$

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

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

$x = - 3 - 3$

$y = - 3$

Simplify $x = - 3 - 3$ .

Simplify the left side.

Remove parentheses.

$x = - 3 - 3$

$y = - 3$

$x = - 3 - 3$

$y = - 3$

Simplify the right side.

Subtract $3$ from $- 3$ .

$x = - 6$

$y = - 3$

$x = - 6$

$y = - 3$

$x = - 6$

$y = - 3$

$x = - 6$

$y = - 3$

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

$(- 6, - 3)$

The result can be shown in multiple forms.

Point Form:

$(- 6, - 3)$

Equation Form:

$x = - 6, y = - 3$

Solve the System of Equations x-y=-3 -8x+y=45

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