Solve by Substitution 2x+y=-2 and 5x+3y=-8

$2 x + y = - 2$ and $5 x + 3 y = - 8$

Subtract $2 x$ from both sides of the equation.

$y = - 2 - 2 x$

$5 x + 3 y = - 8$

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

Replace all occurrences of $y$ in $5 x + 3 y = - 8$ with $- 2 - 2 x$ .

$5 x + 3 (- 2 - 2 x) = - 8$

$y = - 2 - 2 x$

Simplify the left side.

Simplify $5 x + 3 (- 2 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$5 x + 3 \cdot - 2 + 3 (- 2 x) = - 8$

$y = - 2 - 2 x$

Multiply $3$ by $- 2$ .

$5 x - 6 + 3 (- 2 x) = - 8$

$y = - 2 - 2 x$

Multiply $- 2$ by $3$ .

$5 x - 6 - 6 x = - 8$

$y = - 2 - 2 x$

$5 x - 6 - 6 x = - 8$

$y = - 2 - 2 x$

Subtract $6 x$ from $5 x$ .

$- x - 6 = - 8$

$y = - 2 - 2 x$

$- x - 6 = - 8$

$y = - 2 - 2 x$

$- x - 6 = - 8$

$y = - 2 - 2 x$

$- x - 6 = - 8$

$y = - 2 - 2 x$

Solve for $x$ in $- x - 6 = - 8$ .

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

Add $6$ to both sides of the equation.

$- x = - 8 + 6$

$y = - 2 - 2 x$

Add $- 8$ and $6$ .

$- x = - 2$

$y = - 2 - 2 x$

$- x = - 2$

$y = - 2 - 2 x$

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

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

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

$y = - 2 - 2 x$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$y = - 2 - 2 x$

Divide $x$ by $1$ .

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

$y = - 2 - 2 x$

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

$y = - 2 - 2 x$

Simplify the right side.

Divide $- 2$ by $- 1$ .

$x = 2$

$y = - 2 - 2 x$

$x = 2$

$y = - 2 - 2 x$

$x = 2$

$y = - 2 - 2 x$

$x = 2$

$y = - 2 - 2 x$

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

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

$y = - 2 - 2 \cdot 2$

$x = 2$

Simplify the right side.

Simplify $- 2 - 2 \cdot 2$ .

Multiply $- 2$ by $2$ .

$y = - 2 - 4$

$x = 2$

Subtract $4$ from $- 2$ .

$y = - 6$

$x = 2$

$y = - 6$

$x = 2$

$y = - 6$

$x = 2$

$y = - 6$

$x = 2$

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

$(2, - 6)$

The result can be shown in multiple forms.

Point Form:

$(2, - 6)$

Equation Form:

$x = 2, y = - 6$

Solve by Substitution 2x+y=-2 and 5x+3y=-8

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