Solve the System of Equations y=x+1 3x+y=-7

$y = x + 1$ $3 x + y = - 7$

Step 1

Replace all occurrences of $y$ with $x + 1$ in each equation.

Replace all occurrences of $y$ in $3 x + y = - 7$ with $x + 1$ .

$3 x + x + 1 = - 7$

$y = x + 1$

Simplify the left side.

Simplify $3 x + x + 1$ .

Remove parentheses.

$3 x + x + 1 = - 7$

$y = x + 1$

Add $3 x$ and $x$ .

$4 x + 1 = - 7$

$y = x + 1$

$4 x + 1 = - 7$

$y = x + 1$

$4 x + 1 = - 7$

$y = x + 1$

$4 x + 1 = - 7$

$y = x + 1$

Step 2

Solve for $x$ in $4 x + 1 = - 7$ .

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

Subtract $1$ from both sides of the equation.

$4 x = - 7 - 1$

$y = x + 1$

Subtract $1$ from $- 7$ .

$4 x = - 8$

$y = x + 1$

$4 x = - 8$

$y = x + 1$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

$y = x + 1$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

$y = x + 1$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

$y = x + 1$

$x = \frac{- 8}{4}$

$y = x + 1$

$x = \frac{- 8}{4}$

$y = x + 1$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$

$y = x + 1$

$x = - 2$

$y = x + 1$

$x = - 2$

$y = x + 1$

$x = - 2$

$y = x + 1$

Step 3

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

Replace all occurrences of $x$ in $y = x + 1$ with $- 2$ .

$y = (- 2) + 1$

$x = - 2$

Simplify the right side.

Add $- 2$ and $1$ .

$y = - 1$

$x = - 2$

$y = - 1$

$x = - 2$

$y = - 1$

$x = - 2$

Step 4

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

$(- 2, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 2, - 1)$

Equation Form:

$x = - 2, y = - 1$

Step 6

Solve the System of Equations y=x+1 3x+y=-7

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