Solve the System of Equations x+y=5 y=x+1

$x + y = 5$ $y = x + 1$

Step 1

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

Replace all occurrences of $y$ in $x + y = 5$ with $x + 1$ .

$x + x + 1 = 5$

$y = x + 1$

Simplify the left side.

Simplify $x + x + 1$ .

Remove parentheses.

$x + x + 1 = 5$

$y = x + 1$

Add $x$ and $x$ .

$2 x + 1 = 5$

$y = x + 1$

$2 x + 1 = 5$

$y = x + 1$

$2 x + 1 = 5$

$y = x + 1$

$2 x + 1 = 5$

$y = x + 1$

Step 2

Solve for $x$ in $2 x + 1 = 5$ .

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

Subtract $1$ from both sides of the equation.

$2 x = 5 - 1$

$y = x + 1$

Subtract $1$ from $5$ .

$2 x = 4$

$y = x + 1$

$2 x = 4$

$y = x + 1$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

$y = x + 1$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

$y = x + 1$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

$y = x + 1$

$x = \frac{4}{2}$

$y = x + 1$

$x = \frac{4}{2}$

$y = x + 1$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

$y = x + 1$

$x = 2$

$y = x + 1$

$x = 2$

$y = x + 1$

$x = 2$

$y = x + 1$

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 $1$ .

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

Step 4

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

$(2, 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 6

Solve the System of Equations x+y=5 y=x+1

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