Solve the System of Equations y=2x+1 x-y=-3

$y = 2 x + 1$ $x - y = - 3$

Replace all occurrences of $y$ with $2 x + 1$ in each equation.

Replace all occurrences of $y$ in $x - y = - 3$ with $2 x + 1$ .

$x - (2 x + 1) = - 3$

$y = 2 x + 1$

Simplify the left side.

Simplify $x - (2 x + 1)$ .

Simplify each term.

Apply the distributive property.

$x - (2 x) - 1 \cdot 1 = - 3$

$y = 2 x + 1$

Multiply $2$ by $- 1$ .

$x - 2 x - 1 \cdot 1 = - 3$

$y = 2 x + 1$

Multiply $- 1$ by $1$ .

$x - 2 x - 1 = - 3$

$y = 2 x + 1$

$x - 2 x - 1 = - 3$

$y = 2 x + 1$

Subtract $2 x$ from $x$ .

$- x - 1 = - 3$

$y = 2 x + 1$

$- x - 1 = - 3$

$y = 2 x + 1$

$- x - 1 = - 3$

$y = 2 x + 1$

$- x - 1 = - 3$

$y = 2 x + 1$

Solve for $x$ in $- x - 1 = - 3$ .

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

Add $1$ to both sides of the equation.

$- x = - 3 + 1$

$y = 2 x + 1$

Add $- 3$ and $1$ .

$- x = - 2$

$y = 2 x + 1$

$- x = - 2$

$y = 2 x + 1$

Divide each term in $- x = - 2$ by $- 1$ and simplify.

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

$y = 2 x + 1$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 2}{- 1}$

$y = 2 x + 1$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

$y = 2 x + 1$

$x = \frac{- 2}{- 1}$

$y = 2 x + 1$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

$y = 2 x + 1$

$x = 2$

$y = 2 x + 1$

$x = 2$

$y = 2 x + 1$

$x = 2$

$y = 2 x + 1$

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

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

$y = 2 (2) + 1$

$x = 2$

Simplify the right side.

Simplify $2 (2) + 1$ .

Multiply $2$ by $2$ .

$y = 4 + 1$

$x = 2$

Add $4$ and $1$ .

$y = 5$

$x = 2$

$y = 5$

$x = 2$

$y = 5$

$x = 2$

$y = 5$

$x = 2$

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

$(2, 5)$

The result can be shown in multiple forms.

Point Form:

$(2, 5)$

Equation Form:

$x = 2, y = 5$

Solve the System of Equations y=2x+1 x-y=-3

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