Solve the System of Equations 5x-5y=0 and 4x-6y=-18

$5 x - 5 y = 0$ and $4 x - 6 y = - 18$

Step 1

Solve for $x$ in $5 x - 5 y = 0$ .

Add $5 y$ to both sides of the equation.

$5 x = 5 y$

$4 x - 6 y = - 18$

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

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

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

$4 x - 6 y = - 18$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$4 x - 6 y = - 18$

Divide $x$ by $1$ .

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

$4 x - 6 y = - 18$

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

$4 x - 6 y = - 18$

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

$4 x - 6 y = - 18$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$4 x - 6 y = - 18$

Divide $y$ by $1$ .

$x = y$

$4 x - 6 y = - 18$

$x = y$

$4 x - 6 y = - 18$

$x = y$

$4 x - 6 y = - 18$

$x = y$

$4 x - 6 y = - 18$

$x = y$

$4 x - 6 y = - 18$

Step 2

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

Replace all occurrences of $x$ in $4 x - 6 y = - 18$ with $y$ .

$4 (y) - 6 y = - 18$

$x = y$

Simplify the left side.

Subtract $6 y$ from $4 y$ .

$- 2 y = - 18$

$x = y$

$- 2 y = - 18$

$x = y$

$- 2 y = - 18$

$x = y$

Step 3

Divide each term in $- 2 y = - 18$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 18$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 18}{- 2}$

$x = y$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 18}{- 2}$

$x = y$

Divide $y$ by $1$ .

$y = \frac{- 18}{- 2}$

$x = y$

$y = \frac{- 18}{- 2}$

$x = y$

$y = \frac{- 18}{- 2}$

$x = y$

Simplify the right side.

Divide $- 18$ by $- 2$ .

$y = 9$

$x = y$

$y = 9$

$x = y$

$y = 9$

$x = y$

Step 4

Replace all occurrences of $y$ with $9$ in each equation.

Replace all occurrences of $y$ in $x = y$ with $9$ .

$x = 9$

$y = 9$

Simplify the left side.

Remove parentheses.

$x = 9$

$y = 9$

$x = 9$

$y = 9$

$x = 9$

$y = 9$

Step 5

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

$(9, 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(9, 9)$

Equation Form:

$x = 9, y = 9$

Step 7

Solve the System of Equations 5x-5y=0 and 4x-6y=-18

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