Solve the System of Equations y=x-5 -x-3y=7

$y = x - 5$ $- x - 3 y = 7$

Step 1

Replace all occurrences of $y$ with $x - 5$ in each equation.

Replace all occurrences of $y$ in $- x - 3 y = 7$ with $x - 5$ .

$- x - 3 (x - 5) = 7$

$y = x - 5$

Simplify the left side.

Simplify $- x - 3 (x - 5)$ .

Simplify each term.

Apply the distributive property.

$- x - 3 x - 3 \cdot - 5 = 7$

$y = x - 5$

Multiply $- 3$ by $- 5$ .

$- x - 3 x + 15 = 7$

$y = x - 5$

$- x - 3 x + 15 = 7$

$y = x - 5$

Subtract $3 x$ from $- x$ .

$- 4 x + 15 = 7$

$y = x - 5$

$- 4 x + 15 = 7$

$y = x - 5$

$- 4 x + 15 = 7$

$y = x - 5$

$- 4 x + 15 = 7$

$y = x - 5$

Step 2

Solve for $x$ in $- 4 x + 15 = 7$ .

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

Subtract $15$ from both sides of the equation.

$- 4 x = 7 - 15$

$y = x - 5$

Subtract $15$ from $7$ .

$- 4 x = - 8$

$y = x - 5$

$- 4 x = - 8$

$y = x - 5$

Divide each term in $- 4 x = - 8$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 8$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 8}{- 4}$

$y = x - 5$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 8}{- 4}$

$y = x - 5$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 4}$

$y = x - 5$

$x = \frac{- 8}{- 4}$

$y = x - 5$

$x = \frac{- 8}{- 4}$

$y = x - 5$

Simplify the right side.

Divide $- 8$ by $- 4$ .

$x = 2$

$y = x - 5$

$x = 2$

$y = x - 5$

$x = 2$

$y = x - 5$

$x = 2$

$y = x - 5$

Step 3

Replace all occurrences of $x$ with $2$ in each equation.

Replace all occurrences of $x$ in $y = x - 5$ with $2$ .

$y = (2) - 5$

$x = 2$

Simplify the right side.

Subtract $5$ from $2$ .

$y = - 3$

$x = 2$

$y = - 3$

$x = 2$

$y = - 3$

$x = 2$

Step 4

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

$(2, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, - 3)$

Equation Form:

$x = 2, y = - 3$

Step 6

Solve the System of Equations y=x-5 -x-3y=7

Related Questions

Support LCMGCF.com by disabling your adblocker.