Solve the System of Equations x+y=7 2x+3y=5

$x + y = 7$ $2 x + 3 y = 5$

Step 1

Subtract $y$ from both sides of the equation.

$x = 7 - y$

$2 x + 3 y = 5$

Step 2

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

Replace all occurrences of $x$ in $2 x + 3 y = 5$ with $7 - y$ .

$2 (7 - y) + 3 y = 5$

$x = 7 - y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$2 \cdot 7 + 2 (- y) + 3 y = 5$

$x = 7 - y$

Multiply $2$ by $7$ .

$14 + 2 (- y) + 3 y = 5$

$x = 7 - y$

Multiply $- 1$ by $2$ .

$14 - 2 y + 3 y = 5$

$x = 7 - y$

$14 - 2 y + 3 y = 5$

$x = 7 - y$

Add $- 2 y$ and $3 y$ .

$14 + y = 5$

$x = 7 - y$

$14 + y = 5$

$x = 7 - y$

$14 + y = 5$

$x = 7 - y$

$14 + y = 5$

$x = 7 - y$

Step 3

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

Subtract $14$ from both sides of the equation.

$y = 5 - 14$

$x = 7 - y$

Subtract $14$ from $5$ .

$y = - 9$

$x = 7 - y$

$y = - 9$

$x = 7 - y$

Step 4

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

Replace all occurrences of $y$ in $x = 7 - y$ with $- 9$ .

$x = 7 - (- 9)$

$y = - 9$

Simplify the right side.

Simplify $7 - (- 9)$ .

Multiply $- 1$ by $- 9$ .

$x = 7 + 9$

$y = - 9$

Add $7$ and $9$ .

$x = 16$

$y = - 9$

$x = 16$

$y = - 9$

$x = 16$

$y = - 9$

$x = 16$

$y = - 9$

Step 5

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

$(16, - 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(16, - 9)$

Equation Form:

$x = 16, y = - 9$

Step 7

Solve the System of Equations x+y=7 2x+3y=5

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