Solve by Substitution x+7y=-2 , 3x+y=34

$x + 7 y = - 2$ , $3 x + y = 34$

Step 1

Subtract $7 y$ from both sides of the equation.

$x = - 2 - 7 y$

$3 x + y = 34$

Step 2

Replace all occurrences of $x$ with $- 2 - 7 y$ in each equation.

Replace all occurrences of $x$ in $3 x + y = 34$ with $- 2 - 7 y$ .

$3 (- 2 - 7 y) + y = 34$

$x = - 2 - 7 y$

Simplify the left side.

Simplify $3 (- 2 - 7 y) + y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot - 2 + 3 (- 7 y) + y = 34$

$x = - 2 - 7 y$

Multiply $3$ by $- 2$ .

$- 6 + 3 (- 7 y) + y = 34$

$x = - 2 - 7 y$

Multiply $- 7$ by $3$ .

$- 6 - 21 y + y = 34$

$x = - 2 - 7 y$

$- 6 - 21 y + y = 34$

$x = - 2 - 7 y$

Add $- 21 y$ and $y$ .

$- 6 - 20 y = 34$

$x = - 2 - 7 y$

$- 6 - 20 y = 34$

$x = - 2 - 7 y$

$- 6 - 20 y = 34$

$x = - 2 - 7 y$

$- 6 - 20 y = 34$

$x = - 2 - 7 y$

Step 3

Solve for $y$ in $- 6 - 20 y = 34$ .

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

Add $6$ to both sides of the equation.

$- 20 y = 34 + 6$

$x = - 2 - 7 y$

Add $34$ and $6$ .

$- 20 y = 40$

$x = - 2 - 7 y$

$- 20 y = 40$

$x = - 2 - 7 y$

Divide each term in $- 20 y = 40$ by $- 20$ and simplify.

Divide each term in $- 20 y = 40$ by $- 20$ .

$\frac{- 20 y}{- 20} = \frac{40}{- 20}$

$x = - 2 - 7 y$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 y}{- 20} = \frac{40}{- 20}$

$x = - 2 - 7 y$

Divide $y$ by $1$ .

$y = \frac{40}{- 20}$

$x = - 2 - 7 y$

$y = \frac{40}{- 20}$

$x = - 2 - 7 y$

$y = \frac{40}{- 20}$

$x = - 2 - 7 y$

Simplify the right side.

Divide $40$ by $- 20$ .

$y = - 2$

$x = - 2 - 7 y$

$y = - 2$

$x = - 2 - 7 y$

$y = - 2$

$x = - 2 - 7 y$

$y = - 2$

$x = - 2 - 7 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 2 - 7 y$ with $- 2$ .

$x = - 2 - 7 \cdot - 2$

$y = - 2$

Simplify the right side.

Simplify $- 2 - 7 \cdot - 2$ .

Multiply $- 7$ by $- 2$ .

$x = - 2 + 14$

$y = - 2$

Add $- 2$ and $14$ .

$x = 12$

$y = - 2$

$x = 12$

$y = - 2$

$x = 12$

$y = - 2$

$x = 12$

$y = - 2$

Step 5

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

$(12, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(12, - 2)$

Equation Form:

$x = 12, y = - 2$

Step 7

Solve by Substitution x+7y=-2 , 3x+y=34

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