Solve by Substitution x=7-2y 2x+y=5

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

Step 1

Reorder $7$ and $- 2 y$ .

$x = - 2 y + 7$

$2 x + y = 5$

Step 2

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

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

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

$x = - 2 y + 7$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$x = - 2 y + 7$

Multiply $- 2$ by $2$ .

$- 4 y + 2 \cdot 7 + y = 5$

$x = - 2 y + 7$

Multiply $2$ by $7$ .

$- 4 y + 14 + y = 5$

$x = - 2 y + 7$

$- 4 y + 14 + y = 5$

$x = - 2 y + 7$

Add $- 4 y$ and $y$ .

$- 3 y + 14 = 5$

$x = - 2 y + 7$

$- 3 y + 14 = 5$

$x = - 2 y + 7$

$- 3 y + 14 = 5$

$x = - 2 y + 7$

$- 3 y + 14 = 5$

$x = - 2 y + 7$

Step 3

Solve for $y$ in $- 3 y + 14 = 5$ .

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

Subtract $14$ from both sides of the equation.

$- 3 y = 5 - 14$

$x = - 2 y + 7$

Subtract $14$ from $5$ .

$- 3 y = - 9$

$x = - 2 y + 7$

$- 3 y = - 9$

$x = - 2 y + 7$

Divide each term in $- 3 y = - 9$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 9$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

$x = - 2 y + 7$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 9}{- 3}$

$x = - 2 y + 7$

Divide $y$ by $1$ .

$y = \frac{- 9}{- 3}$

$x = - 2 y + 7$

$y = \frac{- 9}{- 3}$

$x = - 2 y + 7$

$y = \frac{- 9}{- 3}$

$x = - 2 y + 7$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$y = 3$

$x = - 2 y + 7$

$y = 3$

$x = - 2 y + 7$

$y = 3$

$x = - 2 y + 7$

$y = 3$

$x = - 2 y + 7$

Step 4

Replace all occurrences of $y$ with $3$ in each equation.

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

$x = - 2 \cdot 3 + 7$

$y = 3$

Simplify the right side.

Simplify $- 2 \cdot 3 + 7$ .

Multiply $- 2$ by $3$ .

$x = - 6 + 7$

$y = 3$

Add $- 6$ and $7$ .

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

$x = 1$

$y = 3$

Step 5

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

$(1, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 3)$

Equation Form:

$x = 1, y = 3$

Step 7

Solve by Substitution x=7-2y 2x+y=5

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