Solve by Substitution -2x+3y=14 , x+2y=7

$- 2 x + 3 y = 14$ , $x + 2 y = 7$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 7 - 2 y$

$- 2 x + 3 y = 14$

Step 2

Replace all occurrences of $x$ with $7 - 2 y$ in each equation.

Replace all occurrences of $x$ in $- 2 x + 3 y = 14$ with $7 - 2 y$ .

$- 2 (7 - 2 y) + 3 y = 14$

$x = 7 - 2 y$

Simplify the left side.

Simplify $- 2 (7 - 2 y) + 3 y$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot 7 - 2 (- 2 y) + 3 y = 14$

$x = 7 - 2 y$

Multiply $- 2$ by $7$ .

$- 14 - 2 (- 2 y) + 3 y = 14$

$x = 7 - 2 y$

Multiply $- 2$ by $- 2$ .

$- 14 + 4 y + 3 y = 14$

$x = 7 - 2 y$

$- 14 + 4 y + 3 y = 14$

$x = 7 - 2 y$

Add $4 y$ and $3 y$ .

$- 14 + 7 y = 14$

$x = 7 - 2 y$

$- 14 + 7 y = 14$

$x = 7 - 2 y$

$- 14 + 7 y = 14$

$x = 7 - 2 y$

$- 14 + 7 y = 14$

$x = 7 - 2 y$

Step 3

Solve for $y$ in $- 14 + 7 y = 14$ .

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

Add $14$ to both sides of the equation.

$7 y = 14 + 14$

$x = 7 - 2 y$

Add $14$ and $14$ .

$7 y = 28$

$x = 7 - 2 y$

$7 y = 28$

$x = 7 - 2 y$

Divide each term in $7 y = 28$ by $7$ and simplify.

Divide each term in $7 y = 28$ by $7$ .

$\frac{7 y}{7} = \frac{28}{7}$

$x = 7 - 2 y$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{28}{7}$

$x = 7 - 2 y$

Divide $y$ by $1$ .

$y = \frac{28}{7}$

$x = 7 - 2 y$

$y = \frac{28}{7}$

$x = 7 - 2 y$

$y = \frac{28}{7}$

$x = 7 - 2 y$

Simplify the right side.

Divide $28$ by $7$ .

$y = 4$

$x = 7 - 2 y$

$y = 4$

$x = 7 - 2 y$

$y = 4$

$x = 7 - 2 y$

$y = 4$

$x = 7 - 2 y$

Step 4

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x = 7 - 2 y$ with $4$ .

$x = 7 - 2 \cdot 4$

$y = 4$

Simplify the right side.

Simplify $7 - 2 \cdot 4$ .

Multiply $- 2$ by $4$ .

$x = 7 - 8$

$y = 4$

Subtract $8$ from $7$ .

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

Step 5

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

$(- 1, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, 4)$

Equation Form:

$x = - 1, y = 4$

Step 7

Solve by Substitution -2x+3y=14 , x+2y=7

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