Solve by Substitution 2x+4y=11 3x+6y=17

$2 x + 4 y = 11$ $3 x + 6 y = 17$

Step 1

Solve for $x$ in $2 x + 4 y = 11$ .

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

$2 x = 11 - 4 y$

$3 x + 6 y = 17$

Divide each term in $2 x = 11 - 4 y$ by $2$ and simplify.

Divide each term in $2 x = 11 - 4 y$ by $2$ .

$\frac{2 x}{2} = \frac{11}{2} + \frac{- 4 y}{2}$

$3 x + 6 y = 17$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{11}{2} + \frac{- 4 y}{2}$

$3 x + 6 y = 17$

Divide $x$ by $1$ .

$x = \frac{11}{2} + \frac{- 4 y}{2}$

$3 x + 6 y = 17$

$x = \frac{11}{2} + \frac{- 4 y}{2}$

$3 x + 6 y = 17$

$x = \frac{11}{2} + \frac{- 4 y}{2}$

$3 x + 6 y = 17$

Simplify the right side.

Cancel the common factor of $- 4$ and $2$ .

Factor $2$ out of $- 4 y$ .

$x = \frac{11}{2} + \frac{2 (- 2 y)}{2}$

$3 x + 6 y = 17$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = \frac{11}{2} + \frac{2 (- 2 y)}{2 (1)}$

$3 x + 6 y = 17$

Cancel the common factor.

$x = \frac{11}{2} + \frac{2 (- 2 y)}{2 \cdot 1}$

$3 x + 6 y = 17$

Rewrite the expression.

$x = \frac{11}{2} + \frac{- 2 y}{1}$

$3 x + 6 y = 17$

Divide $- 2 y$ by $1$ .

$x = \frac{11}{2} - 2 y$

$3 x + 6 y = 17$

$x = \frac{11}{2} - 2 y$

$3 x + 6 y = 17$

$x = \frac{11}{2} - 2 y$

$3 x + 6 y = 17$

$x = \frac{11}{2} - 2 y$

$3 x + 6 y = 17$

$x = \frac{11}{2} - 2 y$

$3 x + 6 y = 17$

$x = \frac{11}{2} - 2 y$

$3 x + 6 y = 17$

Step 2

Replace all occurrences of $x$ with $\frac{11}{2} - 2 y$ in each equation.

Replace all occurrences of $x$ in $3 x + 6 y = 17$ with $\frac{11}{2} - 2 y$ .

$3 (\frac{11}{2} - 2 y) + 6 y = 17$

$x = \frac{11}{2} - 2 y$

Simplify the left side.

Simplify $3 (\frac{11}{2} - 2 y) + 6 y$ .

Simplify each term.

Apply the distributive property.

$3 (\frac{11}{2}) + 3 (- 2 y) + 6 y = 17$

$x = \frac{11}{2} - 2 y$

Multiply $3 (\frac{11}{2})$ .

Combine $3$ and $\frac{11}{2}$ .

$\frac{3 \cdot 11}{2} + 3 (- 2 y) + 6 y = 17$

$x = \frac{11}{2} - 2 y$

Multiply $3$ by $11$ .

$\frac{33}{2} + 3 (- 2 y) + 6 y = 17$

$x = \frac{11}{2} - 2 y$

$\frac{33}{2} + 3 (- 2 y) + 6 y = 17$

$x = \frac{11}{2} - 2 y$

Multiply $- 2$ by $3$ .

$\frac{33}{2} - 6 y + 6 y = 17$

$x = \frac{11}{2} - 2 y$

$\frac{33}{2} - 6 y + 6 y = 17$

$x = \frac{11}{2} - 2 y$

Combine the opposite terms in $\frac{33}{2} - 6 y + 6 y$ .

Add $- 6 y$ and $6 y$ .

$\frac{33}{2} + 0 = 17$

$x = \frac{11}{2} - 2 y$

Add $\frac{33}{2}$ and $0$ .

$\frac{33}{2} = 17$

$x = \frac{11}{2} - 2 y$

$\frac{33}{2} = 17$

$x = \frac{11}{2} - 2 y$

$\frac{33}{2} = 17$

$x = \frac{11}{2} - 2 y$

$\frac{33}{2} = 17$

$x = \frac{11}{2} - 2 y$

$\frac{33}{2} = 17$

$x = \frac{11}{2} - 2 y$

Step 3

Since $\frac{33}{2} = 17$ is not true, there is no solution.

No solution

Step 4

Solve by Substitution 2x+4y=11 3x+6y=17

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