Solve the System of Equations 4x+y=0 2y+x=-7

$4 x + y = 0$ $2 y + x = - 7$

Step 1

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

$y = - 4 x$

$2 y + x = - 7$

Step 2

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

Replace all occurrences of $y$ in $2 y + x = - 7$ with $- 4 x$ .

$2 (- 4 x) + x = - 7$

$y = - 4 x$

Simplify the left side.

Simplify $2 (- 4 x) + x$ .

Multiply $- 4$ by $2$ .

$- 8 x + x = - 7$

$y = - 4 x$

Add $- 8 x$ and $x$ .

$- 7 x = - 7$

$y = - 4 x$

$- 7 x = - 7$

$y = - 4 x$

$- 7 x = - 7$

$y = - 4 x$

$- 7 x = - 7$

$y = - 4 x$

Step 3

Divide each term in $- 7 x = - 7$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 7$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 7}{- 7}$

$y = - 4 x$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 7}{- 7}$

$y = - 4 x$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 7}$

$y = - 4 x$

$x = \frac{- 7}{- 7}$

$y = - 4 x$

$x = \frac{- 7}{- 7}$

$y = - 4 x$

Simplify the right side.

Divide $- 7$ by $- 7$ .

$x = 1$

$y = - 4 x$

$x = 1$

$y = - 4 x$

$x = 1$

$y = - 4 x$

Step 4

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

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

$y = - 4 \cdot 1$

$x = 1$

Simplify the right side.

Multiply $- 4$ by $1$ .

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

$y = - 4$

$x = 1$

Step 5

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

$(1, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, - 4)$

Equation Form:

$x = 1, y = - 4$

Step 7

Solve the System of Equations 4x+y=0 2y+x=-7

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