Solve the System of Equations x+y=3 y=x-5

$x + y = 3$ $y = x - 5$

Step 1

Replace all occurrences of $y$ with $x - 5$ in each equation.

Replace all occurrences of $y$ in $x + y = 3$ with $x - 5$ .

$x + x - 5 = 3$

$y = x - 5$

Simplify the left side.

Simplify $x + x - 5$ .

Remove parentheses.

$x + x - 5 = 3$

$y = x - 5$

Add $x$ and $x$ .

$2 x - 5 = 3$

$y = x - 5$

$2 x - 5 = 3$

$y = x - 5$

$2 x - 5 = 3$

$y = x - 5$

$2 x - 5 = 3$

$y = x - 5$

Step 2

Solve for $x$ in $2 x - 5 = 3$ .

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

Add $5$ to both sides of the equation.

$2 x = 3 + 5$

$y = x - 5$

Add $3$ and $5$ .

$2 x = 8$

$y = x - 5$

$2 x = 8$

$y = x - 5$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

$y = x - 5$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

$y = x - 5$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

$y = x - 5$

$x = \frac{8}{2}$

$y = x - 5$

$x = \frac{8}{2}$

$y = x - 5$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$

$y = x - 5$

$x = 4$

$y = x - 5$

$x = 4$

$y = x - 5$

$x = 4$

$y = x - 5$

Step 3

Replace all occurrences of $x$ with $4$ in each equation.

Replace all occurrences of $x$ in $y = x - 5$ with $4$ .

$y = (4) - 5$

$x = 4$

Simplify the right side.

Subtract $5$ from $4$ .

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

$y = - 1$

$x = 4$

Step 4

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

$(4, - 1)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, - 1)$

Equation Form:

$x = 4, y = - 1$

Step 6

Solve the System of Equations x+y=3 y=x-5

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