Solve the System of Equations x+y=5 -5x-4y=-18

$x + y = 5$ $- 5 x - 4 y = - 18$

Step 1

Subtract $y$ from both sides of the equation.

$x = 5 - y$

$- 5 x - 4 y = - 18$

Step 2

Replace all occurrences of $x$ with $5 - y$ in each equation.

Replace all occurrences of $x$ in $- 5 x - 4 y = - 18$ with $5 - y$ .

$- 5 (5 - y) - 4 y = - 18$

$x = 5 - y$

Simplify the left side.

Simplify $- 5 (5 - y) - 4 y$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot 5 - 5 (- y) - 4 y = - 18$

$x = 5 - y$

Multiply $- 5$ by $5$ .

$- 25 - 5 (- y) - 4 y = - 18$

$x = 5 - y$

Multiply $- 1$ by $- 5$ .

$- 25 + 5 y - 4 y = - 18$

$x = 5 - y$

$- 25 + 5 y - 4 y = - 18$

$x = 5 - y$

Subtract $4 y$ from $5 y$ .

$- 25 + y = - 18$

$x = 5 - y$

$- 25 + y = - 18$

$x = 5 - y$

$- 25 + y = - 18$

$x = 5 - y$

$- 25 + y = - 18$

$x = 5 - y$

Step 3

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

Add $25$ to both sides of the equation.

$y = - 18 + 25$

$x = 5 - y$

Add $- 18$ and $25$ .

$y = 7$

$x = 5 - y$

$y = 7$

$x = 5 - y$

Step 4

Replace all occurrences of $y$ with $7$ in each equation.

Replace all occurrences of $y$ in $x = 5 - y$ with $7$ .

$x = 5 - (7)$

$y = 7$

Simplify the right side.

Simplify $5 - (7)$ .

Multiply $- 1$ by $7$ .

$x = 5 - 7$

$y = 7$

Subtract $7$ from $5$ .

$x = - 2$

$y = 7$

$x = - 2$

$y = 7$

$x = - 2$

$y = 7$

$x = - 2$

$y = 7$

Step 5

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

$(- 2, 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 7)$

Equation Form:

$x = - 2, y = 7$

Step 7

Solve the System of Equations x+y=5 -5x-4y=-18

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