Solve by Substitution x-4y=27 , 3x+y=-23

$x - 4 y = 27$ , $3 x + y = - 23$

Step 1

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

$x = 27 + 4 y$

$3 x + y = - 23$

Step 2

Replace all occurrences of $x$ with $27 + 4 y$ in each equation.

Replace all occurrences of $x$ in $3 x + y = - 23$ with $27 + 4 y$ .

$3 (27 + 4 y) + y = - 23$

$x = 27 + 4 y$

Simplify the left side.

Simplify $3 (27 + 4 y) + y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 27 + 3 (4 y) + y = - 23$

$x = 27 + 4 y$

Multiply $3$ by $27$ .

$81 + 3 (4 y) + y = - 23$

$x = 27 + 4 y$

Multiply $4$ by $3$ .

$81 + 12 y + y = - 23$

$x = 27 + 4 y$

$81 + 12 y + y = - 23$

$x = 27 + 4 y$

Add $12 y$ and $y$ .

$81 + 13 y = - 23$

$x = 27 + 4 y$

$81 + 13 y = - 23$

$x = 27 + 4 y$

$81 + 13 y = - 23$

$x = 27 + 4 y$

$81 + 13 y = - 23$

$x = 27 + 4 y$

Step 3

Solve for $y$ in $81 + 13 y = - 23$ .

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

Subtract $81$ from both sides of the equation.

$13 y = - 23 - 81$

$x = 27 + 4 y$

Subtract $81$ from $- 23$ .

$13 y = - 104$

$x = 27 + 4 y$

$13 y = - 104$

$x = 27 + 4 y$

Divide each term in $13 y = - 104$ by $13$ and simplify.

Divide each term in $13 y = - 104$ by $13$ .

$\frac{13 y}{13} = \frac{- 104}{13}$

$x = 27 + 4 y$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 y}{13} = \frac{- 104}{13}$

$x = 27 + 4 y$

Divide $y$ by $1$ .

$y = \frac{- 104}{13}$

$x = 27 + 4 y$

$y = \frac{- 104}{13}$

$x = 27 + 4 y$

$y = \frac{- 104}{13}$

$x = 27 + 4 y$

Simplify the right side.

Divide $- 104$ by $13$ .

$y = - 8$

$x = 27 + 4 y$

$y = - 8$

$x = 27 + 4 y$

$y = - 8$

$x = 27 + 4 y$

$y = - 8$

$x = 27 + 4 y$

Step 4

Replace all occurrences of $y$ with $- 8$ in each equation.

Replace all occurrences of $y$ in $x = 27 + 4 y$ with $- 8$ .

$x = 27 + 4 (- 8)$

$y = - 8$

Simplify the right side.

Simplify $27 + 4 (- 8)$ .

Multiply $4$ by $- 8$ .

$x = 27 - 32$

$y = - 8$

Subtract $32$ from $27$ .

$x = - 5$

$y = - 8$

$x = - 5$

$y = - 8$

$x = - 5$

$y = - 8$

$x = - 5$

$y = - 8$

Step 5

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

$(- 5, - 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 5, - 8)$

Equation Form:

$x = - 5, y = - 8$

Step 7

Solve by Substitution x-4y=27 , 3x+y=-23

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