Solve by Substitution 5x-y=-6 , -x+y=2

$5 x - y = - 6$ , $- x + y = 2$

Step 1

Add $x$ to both sides of the equation.

$y = 2 + x$

$5 x - y = - 6$

Step 2

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

Replace all occurrences of $y$ in $5 x - y = - 6$ with $2 + x$ .

$5 x - (2 + x) = - 6$

$y = 2 + x$

Simplify the left side.

Simplify $5 x - (2 + x)$ .

Simplify each term.

Apply the distributive property.

$5 x - 1 \cdot 2 - x = - 6$

$y = 2 + x$

Multiply $- 1$ by $2$ .

$5 x - 2 - x = - 6$

$y = 2 + x$

$5 x - 2 - x = - 6$

$y = 2 + x$

Subtract $x$ from $5 x$ .

$4 x - 2 = - 6$

$y = 2 + x$

$4 x - 2 = - 6$

$y = 2 + x$

$4 x - 2 = - 6$

$y = 2 + x$

$4 x - 2 = - 6$

$y = 2 + x$

Step 3

Solve for $x$ in $4 x - 2 = - 6$ .

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

Add $2$ to both sides of the equation.

$4 x = - 6 + 2$

$y = 2 + x$

Add $- 6$ and $2$ .

$4 x = - 4$

$y = 2 + x$

$4 x = - 4$

$y = 2 + x$

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

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

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

$y = 2 + x$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

$y = 2 + x$

Divide $x$ by $1$ .

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

$y = 2 + x$

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

$y = 2 + x$

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

$y = 2 + x$

Simplify the right side.

Divide $- 4$ by $4$ .

$x = - 1$

$y = 2 + x$

$x = - 1$

$y = 2 + x$

$x = - 1$

$y = 2 + x$

$x = - 1$

$y = 2 + x$

Step 4

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

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

$y = 2 - 1$

$x = - 1$

Simplify $y = 2 - 1$ .

Simplify the left side.

Remove parentheses.

$y = 2 - 1$

$x = - 1$

$y = 2 - 1$

$x = - 1$

Simplify the right side.

Subtract $1$ from $2$ .

$y = 1$

$x = - 1$

$y = 1$

$x = - 1$

$y = 1$

$x = - 1$

$y = 1$

$x = - 1$

Step 5

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

$(- 1, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, 1)$

Equation Form:

$x = - 1, y = 1$

Step 7

Solve by Substitution 5x-y=-6 , -x+y=2

Related Questions

Support LCMGCF.com by disabling your adblocker.