Solve the System of Equations y=x-5 2x+y=-2

$y = x - 5$ $2 x + y = - 2$

Step 1

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

Replace all occurrences of $y$ in $2 x + y = - 2$ with $x - 5$ .

$2 x + x - 5 = - 2$

$y = x - 5$

Simplify the left side.

Simplify $2 x + x - 5$ .

Remove parentheses.

$2 x + x - 5 = - 2$

$y = x - 5$

Add $2 x$ and $x$ .

$3 x - 5 = - 2$

$y = x - 5$

$3 x - 5 = - 2$

$y = x - 5$

$3 x - 5 = - 2$

$y = x - 5$

$3 x - 5 = - 2$

$y = x - 5$

Step 2

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

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

Add $5$ to both sides of the equation.

$3 x = - 2 + 5$

$y = x - 5$

Add $- 2$ and $5$ .

$3 x = 3$

$y = x - 5$

$3 x = 3$

$y = x - 5$

Divide each term in $3 x = 3$ by $3$ and simplify.

Divide each term in $3 x = 3$ by $3$ .

$\frac{3 x}{3} = \frac{3}{3}$

$y = x - 5$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{3}{3}$

$y = x - 5$

Divide $x$ by $1$ .

$x = \frac{3}{3}$

$y = x - 5$

$x = \frac{3}{3}$

$y = x - 5$

$x = \frac{3}{3}$

$y = x - 5$

Simplify the right side.

Divide $3$ by $3$ .

$x = 1$

$y = x - 5$

$x = 1$

$y = x - 5$

$x = 1$

$y = x - 5$

$x = 1$

$y = x - 5$

Step 3

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

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

$y = (1) - 5$

$x = 1$

Simplify the right side.

Subtract $5$ from $1$ .

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

Step 4

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

$(1, - 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, - 4)$

Equation Form:

$x = 1, y = - 4$

Step 6

Solve the System of Equations y=x-5 2x+y=-2

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