Solve the System of Equations 4x-10y=0 4x-9y=-2

$4 x - 10 y = 0$ $4 x - 9 y = - 2$

Solve for $x$ in $4 x - 10 y = 0$ .

Add $10 y$ to both sides of the equation.

$4 x = 10 y$

$4 x - 9 y = - 2$

Divide each term in $4 x = 10 y$ by $4$ and simplify.

Divide each term in $4 x = 10 y$ by $4$ .

$\frac{4 x}{4} = \frac{10 y}{4}$

$4 x - 9 y = - 2$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{10 y}{4}$

$4 x - 9 y = - 2$

Divide $x$ by $1$ .

$x = \frac{10 y}{4}$

$4 x - 9 y = - 2$

$x = \frac{10 y}{4}$

$4 x - 9 y = - 2$

$x = \frac{10 y}{4}$

$4 x - 9 y = - 2$

Simplify the right side.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10 y$ .

$x = \frac{2 (5 y)}{4}$

$4 x - 9 y = - 2$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 (5 y)}{2 (2)}$

$4 x - 9 y = - 2$

Cancel the common factor.

$x = \frac{2 (5 y)}{2 \cdot 2}$

$4 x - 9 y = - 2$

Rewrite the expression.

$x = \frac{5 y}{2}$

$4 x - 9 y = - 2$

$x = \frac{5 y}{2}$

$4 x - 9 y = - 2$

$x = \frac{5 y}{2}$

$4 x - 9 y = - 2$

$x = \frac{5 y}{2}$

$4 x - 9 y = - 2$

$x = \frac{5 y}{2}$

$4 x - 9 y = - 2$

$x = \frac{5 y}{2}$

$4 x - 9 y = - 2$

Replace all occurrences of $x$ with $\frac{5 y}{2}$ in each equation.

Replace all occurrences of $x$ in $4 x - 9 y = - 2$ with $\frac{5 y}{2}$ .

$4 (\frac{5 y}{2}) - 9 y = - 2$

$x = \frac{5 y}{2}$

Simplify the left side.

Simplify $4 (\frac{5 y}{2}) - 9 y$ .

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$2 (2) (\frac{5 y}{2}) - 9 y = - 2$

$x = \frac{5 y}{2}$

Cancel the common factor.

$2 \cdot (2 (\frac{5 y}{2})) - 9 y = - 2$

$x = \frac{5 y}{2}$

Rewrite the expression.

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

$x = \frac{5 y}{2}$

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

$x = \frac{5 y}{2}$

Multiply $5$ by $2$ .

$10 y - 9 y = - 2$

$x = \frac{5 y}{2}$

$10 y - 9 y = - 2$

$x = \frac{5 y}{2}$

Subtract $9 y$ from $10 y$ .

$y = - 2$

$x = \frac{5 y}{2}$

$y = - 2$

$x = \frac{5 y}{2}$

$y = - 2$

$x = \frac{5 y}{2}$

$y = - 2$

$x = \frac{5 y}{2}$

Replace all occurrences of $y$ with $- 2$ in each equation.

Replace all occurrences of $y$ in $x = \frac{5 y}{2}$ with $- 2$ .

$x = \frac{5 (- 2)}{2}$

$y = - 2$

Simplify the right side.

Simplify $\frac{5 (- 2)}{2}$ .

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $5 (- 2)$ .

$x = \frac{2 (5 \cdot (- 1))}{2}$

$y = - 2$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{2 (5 \cdot (- 1))}{2 (1)}$

$y = - 2$

Cancel the common factor.

$x = \frac{2 (5 \cdot (- 1))}{2 \cdot 1}$

$y = - 2$

Rewrite the expression.

$x = \frac{5 \cdot (- 1)}{1}$

$y = - 2$

Divide $5 \cdot (- 1)$ by $1$ .

$x = 5 \cdot (- 1)$

$y = - 2$

$x = 5 \cdot (- 1)$

$y = - 2$

$x = 5 \cdot (- 1)$

$y = - 2$

Multiply $5$ by $- 1$ .

$x = - 5$

$y = - 2$

$x = - 5$

$y = - 2$

$x = - 5$

$y = - 2$

$x = - 5$

$y = - 2$

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

$(- 5, - 2)$

The result can be shown in multiple forms.

Point Form:

$(- 5, - 2)$

Equation Form:

$x = - 5, y = - 2$

Solve the System of Equations 4x-10y=0 4x-9y=-2

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