Solve by Substitution 2x-3y=38 -x-6=y

$2 x - 3 y = 38$ $- x - 6 = y$

Rewrite the equation as $y = - x - 6$ .

$y = - x - 6$

$2 x - 3 y = 38$

Replace all occurrences of $y$ with $- x - 6$ in each equation.

Replace all occurrences of $y$ in $2 x - 3 y = 38$ with $- x - 6$ .

$2 x - 3 (- x - 6) = 38$

$y = - x - 6$

Simplify the left side.

Simplify $2 x - 3 (- x - 6)$ .

Simplify each term.

Apply the distributive property.

$2 x - 3 (- x) - 3 \cdot - 6 = 38$

$y = - x - 6$

Multiply $- 1$ by $- 3$ .

$2 x + 3 x - 3 \cdot - 6 = 38$

$y = - x - 6$

Multiply $- 3$ by $- 6$ .

$2 x + 3 x + 18 = 38$

$y = - x - 6$

$2 x + 3 x + 18 = 38$

$y = - x - 6$

Add $2 x$ and $3 x$ .

$5 x + 18 = 38$

$y = - x - 6$

$5 x + 18 = 38$

$y = - x - 6$

$5 x + 18 = 38$

$y = - x - 6$

$5 x + 18 = 38$

$y = - x - 6$

Solve for $x$ in $5 x + 18 = 38$ .

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

Subtract $18$ from both sides of the equation.

$5 x = 38 - 18$

$y = - x - 6$

Subtract $18$ from $38$ .

$5 x = 20$

$y = - x - 6$

$5 x = 20$

$y = - x - 6$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

$y = - x - 6$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

$y = - x - 6$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

$y = - x - 6$

$x = \frac{20}{5}$

$y = - x - 6$

$x = \frac{20}{5}$

$y = - x - 6$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

$y = - x - 6$

$x = 4$

$y = - x - 6$

$x = 4$

$y = - x - 6$

$x = 4$

$y = - x - 6$

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

Replace all occurrences of $x$ in $y = - x - 6$ with $4$ .

$y = - (4) - 6$

$x = 4$

Simplify the right side.

Simplify $- (4) - 6$ .

Multiply $- 1$ by $4$ .

$y = - 4 - 6$

$x = 4$

Subtract $6$ from $- 4$ .

$y = - 10$

$x = 4$

$y = - 10$

$x = 4$

$y = - 10$

$x = 4$

$y = - 10$

$x = 4$

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

$(4, - 10)$

The result can be shown in multiple forms.

Point Form:

$(4, - 10)$

Equation Form:

$x = 4, y = - 10$

Solve by Substitution 2x-3y=38 -x-6=y

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