Solve by Substitution -4x+y=6 , -5x-y=21

$- 4 x + y = 6$ , $- 5 x - y = 21$

Step 1

Add $4 x$ to both sides of the equation.

$y = 6 + 4 x$

$- 5 x - y = 21$

Step 2

Replace all occurrences of $y$ with $6 + 4 x$ in each equation.

Replace all occurrences of $y$ in $- 5 x - y = 21$ with $6 + 4 x$ .

$- 5 x - (6 + 4 x) = 21$

$y = 6 + 4 x$

Simplify the left side.

Simplify $- 5 x - (6 + 4 x)$ .

Simplify each term.

Apply the distributive property.

$- 5 x - 1 \cdot 6 - (4 x) = 21$

$y = 6 + 4 x$

Multiply $- 1$ by $6$ .

$- 5 x - 6 - (4 x) = 21$

$y = 6 + 4 x$

Multiply $4$ by $- 1$ .

$- 5 x - 6 - 4 x = 21$

$y = 6 + 4 x$

$- 5 x - 6 - 4 x = 21$

$y = 6 + 4 x$

Subtract $4 x$ from $- 5 x$ .

$- 9 x - 6 = 21$

$y = 6 + 4 x$

$- 9 x - 6 = 21$

$y = 6 + 4 x$

$- 9 x - 6 = 21$

$y = 6 + 4 x$

$- 9 x - 6 = 21$

$y = 6 + 4 x$

Step 3

Solve for $x$ in $- 9 x - 6 = 21$ .

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

Add $6$ to both sides of the equation.

$- 9 x = 21 + 6$

$y = 6 + 4 x$

Add $21$ and $6$ .

$- 9 x = 27$

$y = 6 + 4 x$

$- 9 x = 27$

$y = 6 + 4 x$

Divide each term in $- 9 x = 27$ by $- 9$ and simplify.

Divide each term in $- 9 x = 27$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{27}{- 9}$

$y = 6 + 4 x$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{27}{- 9}$

$y = 6 + 4 x$

Divide $x$ by $1$ .

$x = \frac{27}{- 9}$

$y = 6 + 4 x$

$x = \frac{27}{- 9}$

$y = 6 + 4 x$

$x = \frac{27}{- 9}$

$y = 6 + 4 x$

Simplify the right side.

Divide $27$ by $- 9$ .

$x = - 3$

$y = 6 + 4 x$

$x = - 3$

$y = 6 + 4 x$

$x = - 3$

$y = 6 + 4 x$

$x = - 3$

$y = 6 + 4 x$

Step 4

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

Replace all occurrences of $x$ in $y = 6 + 4 x$ with $- 3$ .

$y = 6 + 4 (- 3)$

$x = - 3$

Simplify the right side.

Simplify $6 + 4 (- 3)$ .

Multiply $4$ by $- 3$ .

$y = 6 - 12$

$x = - 3$

Subtract $12$ from $6$ .

$y = - 6$

$x = - 3$

$y = - 6$

$x = - 3$

$y = - 6$

$x = - 3$

$y = - 6$

$x = - 3$

Step 5

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

$(- 3, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, - 6)$

Equation Form:

$x = - 3, y = - 6$

Step 7

Solve by Substitution -4x+y=6 , -5x-y=21

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