Solve the System of Equations 5x+2y=9 x+y=-3

$5 x + 2 y = 9$ $x + y = - 3$

Step 1

Subtract $y$ from both sides of the equation.

$x = - 3 - y$

$5 x + 2 y = 9$

Step 2

Replace all occurrences of $x$ with $- 3 - y$ in each equation.

Replace all occurrences of $x$ in $5 x + 2 y = 9$ with $- 3 - y$ .

$5 (- 3 - y) + 2 y = 9$

$x = - 3 - y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$5 \cdot - 3 + 5 (- y) + 2 y = 9$

$x = - 3 - y$

Multiply $5$ by $- 3$ .

$- 15 + 5 (- y) + 2 y = 9$

$x = - 3 - y$

Multiply $- 1$ by $5$ .

$- 15 - 5 y + 2 y = 9$

$x = - 3 - y$

$- 15 - 5 y + 2 y = 9$

$x = - 3 - y$

Add $- 5 y$ and $2 y$ .

$- 15 - 3 y = 9$

$x = - 3 - y$

$- 15 - 3 y = 9$

$x = - 3 - y$

$- 15 - 3 y = 9$

$x = - 3 - y$

$- 15 - 3 y = 9$

$x = - 3 - y$

Step 3

Solve for $y$ in $- 15 - 3 y = 9$ .

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

Add $15$ to both sides of the equation.

$- 3 y = 9 + 15$

$x = - 3 - y$

Add $9$ and $15$ .

$- 3 y = 24$

$x = - 3 - y$

$- 3 y = 24$

$x = - 3 - y$

Divide each term in $- 3 y = 24$ by $- 3$ and simplify.

Divide each term in $- 3 y = 24$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{24}{- 3}$

$x = - 3 - y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{24}{- 3}$

$x = - 3 - y$

Divide $y$ by $1$ .

$y = \frac{24}{- 3}$

$x = - 3 - y$

$y = \frac{24}{- 3}$

$x = - 3 - y$

$y = \frac{24}{- 3}$

$x = - 3 - y$

Simplify the right side.

Divide $24$ by $- 3$ .

$y = - 8$

$x = - 3 - y$

$y = - 8$

$x = - 3 - y$

$y = - 8$

$x = - 3 - y$

$y = - 8$

$x = - 3 - y$

Step 4

Replace all occurrences of $y$ with $- 8$ in each equation.

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

$x = - 3 - (- 8)$

$y = - 8$

Simplify the right side.

Simplify $- 3 - (- 8)$ .

Multiply $- 1$ by $- 8$ .

$x = - 3 + 8$

$y = - 8$

Add $- 3$ and $8$ .

$x = 5$

$y = - 8$

$x = 5$

$y = - 8$

$x = 5$

$y = - 8$

$x = 5$

$y = - 8$

Step 5

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

$(5, - 8)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, - 8)$

Equation Form:

$x = 5, y = - 8$

Step 7

Solve the System of Equations 5x+2y=9 x+y=-3

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