Solve the System of Equations -4x+11y=15 x=2y

$- 4 x + 11 y = 15$ $x = 2 y$

Step 1

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

Replace all occurrences of $x$ in $- 4 x + 11 y = 15$ with $2 y$ .

$- 4 (2 y) + 11 y = 15$

$x = 2 y$

Simplify the left side.

Simplify $- 4 (2 y) + 11 y$ .

Multiply $2$ by $- 4$ .

$- 8 y + 11 y = 15$

$x = 2 y$

Add $- 8 y$ and $11 y$ .

$3 y = 15$

$x = 2 y$

$3 y = 15$

$x = 2 y$

$3 y = 15$

$x = 2 y$

$3 y = 15$

$x = 2 y$

Step 2

Divide each term in $3 y = 15$ by $3$ and simplify.

Divide each term in $3 y = 15$ by $3$ .

$\frac{3 y}{3} = \frac{15}{3}$

$x = 2 y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{15}{3}$

$x = 2 y$

Divide $y$ by $1$ .

$y = \frac{15}{3}$

$x = 2 y$

$y = \frac{15}{3}$

$x = 2 y$

$y = \frac{15}{3}$

$x = 2 y$

Simplify the right side.

Divide $15$ by $3$ .

$y = 5$

$x = 2 y$

$y = 5$

$x = 2 y$

$y = 5$

$x = 2 y$

Step 3

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

Replace all occurrences of $y$ in $x = 2 y$ with $5$ .

$x = 2 (5)$

$y = 5$

Simplify the right side.

Multiply $2$ by $5$ .

$x = 10$

$y = 5$

$x = 10$

$y = 5$

$x = 10$

$y = 5$

Step 4

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

$(10, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(10, 5)$

Equation Form:

$x = 10, y = 5$

Step 6

Solve the System of Equations -4x+11y=15 x=2y

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