Solve by Substitution x+2y=-13 , 12x+5y=-4

$x + 2 y = - 13$ , $12 x + 5 y = - 4$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = - 13 - 2 y$

$12 x + 5 y = - 4$

Step 2

Replace all occurrences of $x$ with $- 13 - 2 y$ in each equation.

Replace all occurrences of $x$ in $12 x + 5 y = - 4$ with $- 13 - 2 y$ .

$12 (- 13 - 2 y) + 5 y = - 4$

$x = - 13 - 2 y$

Simplify the left side.

Simplify $12 (- 13 - 2 y) + 5 y$ .

Simplify each term.

Apply the distributive property.

$12 \cdot - 13 + 12 (- 2 y) + 5 y = - 4$

$x = - 13 - 2 y$

Multiply $12$ by $- 13$ .

$- 156 + 12 (- 2 y) + 5 y = - 4$

$x = - 13 - 2 y$

Multiply $- 2$ by $12$ .

$- 156 - 24 y + 5 y = - 4$

$x = - 13 - 2 y$

$- 156 - 24 y + 5 y = - 4$

$x = - 13 - 2 y$

Add $- 24 y$ and $5 y$ .

$- 156 - 19 y = - 4$

$x = - 13 - 2 y$

$- 156 - 19 y = - 4$

$x = - 13 - 2 y$

$- 156 - 19 y = - 4$

$x = - 13 - 2 y$

$- 156 - 19 y = - 4$

$x = - 13 - 2 y$

Step 3

Solve for $y$ in $- 156 - 19 y = - 4$ .

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

Add $156$ to both sides of the equation.

$- 19 y = - 4 + 156$

$x = - 13 - 2 y$

Add $- 4$ and $156$ .

$- 19 y = 152$

$x = - 13 - 2 y$

$- 19 y = 152$

$x = - 13 - 2 y$

Divide each term in $- 19 y = 152$ by $- 19$ and simplify.

Divide each term in $- 19 y = 152$ by $- 19$ .

$\frac{- 19 y}{- 19} = \frac{152}{- 19}$

$x = - 13 - 2 y$

Simplify the left side.

Cancel the common factor of $- 19$ .

Cancel the common factor.

$\frac{- 19 y}{- 19} = \frac{152}{- 19}$

$x = - 13 - 2 y$

Divide $y$ by $1$ .

$y = \frac{152}{- 19}$

$x = - 13 - 2 y$

$y = \frac{152}{- 19}$

$x = - 13 - 2 y$

$y = \frac{152}{- 19}$

$x = - 13 - 2 y$

Simplify the right side.

Divide $152$ by $- 19$ .

$y = - 8$

$x = - 13 - 2 y$

$y = - 8$

$x = - 13 - 2 y$

$y = - 8$

$x = - 13 - 2 y$

$y = - 8$

$x = - 13 - 2 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 13 - 2 y$ with $- 8$ .

$x = - 13 - 2 \cdot - 8$

$y = - 8$

Simplify the right side.

Simplify $- 13 - 2 \cdot - 8$ .

Multiply $- 2$ by $- 8$ .

$x = - 13 + 16$

$y = - 8$

Add $- 13$ and $16$ .

$x = 3$

$y = - 8$

$x = 3$

$y = - 8$

$x = 3$

$y = - 8$

$x = 3$

$y = - 8$

Step 5

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

$(3, - 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, - 8)$

Equation Form:

$x = 3, y = - 8$

Step 7

Solve by Substitution x+2y=-13 , 12x+5y=-4

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