Solve by Substitution x-5=y -3x-y=-19

$x - 5 = y$ $- 3 x - y = - 19$

Add $5$ to both sides of the equation.

$x = y + 5$

$- 3 x - y = - 19$

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

Replace all occurrences of $x$ in $- 3 x - y = - 19$ with $y + 5$ .

$- 3 (y + 5) - y = - 19$

$x = y + 5$

Simplify the left side.

Simplify $- 3 (y + 5) - y$ .

Simplify each term.

Apply the distributive property.

$- 3 y - 3 \cdot 5 - y = - 19$

$x = y + 5$

Multiply $- 3$ by $5$ .

$- 3 y - 15 - y = - 19$

$x = y + 5$

$- 3 y - 15 - y = - 19$

$x = y + 5$

Subtract $y$ from $- 3 y$ .

$- 4 y - 15 = - 19$

$x = y + 5$

$- 4 y - 15 = - 19$

$x = y + 5$

$- 4 y - 15 = - 19$

$x = y + 5$

$- 4 y - 15 = - 19$

$x = y + 5$

Solve for $y$ in $- 4 y - 15 = - 19$ .

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

Add $15$ to both sides of the equation.

$- 4 y = - 19 + 15$

$x = y + 5$

Add $- 19$ and $15$ .

$- 4 y = - 4$

$x = y + 5$

$- 4 y = - 4$

$x = y + 5$

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

Divide each term in $- 4 y = - 4$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4}$

$x = y + 5$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4}$

$x = y + 5$

Divide $y$ by $1$ .

$y = \frac{- 4}{- 4}$

$x = y + 5$

$y = \frac{- 4}{- 4}$

$x = y + 5$

$y = \frac{- 4}{- 4}$

$x = y + 5$

Simplify the right side.

Divide $- 4$ by $- 4$ .

$y = 1$

$x = y + 5$

$y = 1$

$x = y + 5$

$y = 1$

$x = y + 5$

$y = 1$

$x = y + 5$

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

Replace all occurrences of $y$ in $x = y + 5$ with $1$ .

$x = (1) + 5$

$y = 1$

Simplify the right side.

Add $1$ and $5$ .

$x = 6$

$y = 1$

$x = 6$

$y = 1$

$x = 6$

$y = 1$

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

$(6, 1)$

The result can be shown in multiple forms.

Point Form:

$(6, 1)$

Equation Form:

$x = 6, y = 1$

Solve by Substitution x-5=y -3x-y=-19

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