Solve the System of Equations 4x+y=-10 and 9x+y=-15

$4 x + y = - 10$ and $9 x + y = - 15$

Step 1

Subtract $4 x$ from both sides of the equation.

$y = - 10 - 4 x$

$9 x + y = - 15$

Step 2

Replace all occurrences of $y$ with $- 10 - 4 x$ in each equation.

Replace all occurrences of $y$ in $9 x + y = - 15$ with $- 10 - 4 x$ .

$9 x - 10 - 4 x = - 15$

$y = - 10 - 4 x$

Simplify the left side.

Simplify $9 x - 10 - 4 x$ .

Remove parentheses.

$9 x - 10 - 4 x = - 15$

$y = - 10 - 4 x$

Subtract $4 x$ from $9 x$ .

$5 x - 10 = - 15$

$y = - 10 - 4 x$

$5 x - 10 = - 15$

$y = - 10 - 4 x$

$5 x - 10 = - 15$

$y = - 10 - 4 x$

$5 x - 10 = - 15$

$y = - 10 - 4 x$

Step 3

Solve for $x$ in $5 x - 10 = - 15$ .

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

Add $10$ to both sides of the equation.

$5 x = - 15 + 10$

$y = - 10 - 4 x$

Add $- 15$ and $10$ .

$5 x = - 5$

$y = - 10 - 4 x$

$5 x = - 5$

$y = - 10 - 4 x$

Divide each term in $5 x = - 5$ by $5$ and simplify.

Divide each term in $5 x = - 5$ by $5$ .

$\frac{5 x}{5} = \frac{- 5}{5}$

$y = - 10 - 4 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 5}{5}$

$y = - 10 - 4 x$

Divide $x$ by $1$ .

$x = \frac{- 5}{5}$

$y = - 10 - 4 x$

$x = \frac{- 5}{5}$

$y = - 10 - 4 x$

$x = \frac{- 5}{5}$

$y = - 10 - 4 x$

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

$y = - 10 - 4 x$

$x = - 1$

$y = - 10 - 4 x$

$x = - 1$

$y = - 10 - 4 x$

$x = - 1$

$y = - 10 - 4 x$

Step 4

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

Replace all occurrences of $x$ in $y = - 10 - 4 x$ with $- 1$ .

$y = - 10 - 4 \cdot - 1$

$x = - 1$

Simplify the right side.

Simplify $- 10 - 4 \cdot - 1$ .

Multiply $- 4$ by $- 1$ .

$y = - 10 + 4$

$x = - 1$

Add $- 10$ and $4$ .

$y = - 6$

$x = - 1$

$y = - 6$

$x = - 1$

$y = - 6$

$x = - 1$

$y = - 6$

$x = - 1$

Step 5

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

$(- 1, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, - 6)$

Equation Form:

$x = - 1, y = - 6$

Step 7

Solve the System of Equations 4x+y=-10 and 9x+y=-15

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