Solve by Substitution x+2y=8 2x+y=7

$x + 2 y = 8$ $2 x + y = 7$

Step 1

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

$x = 8 - 2 y$

$2 x + y = 7$

Step 2

Replace all occurrences of $x$ with $8 - 2 y$ in each equation.

Replace all occurrences of $x$ in $2 x + y = 7$ with $8 - 2 y$ .

$2 (8 - 2 y) + y = 7$

$x = 8 - 2 y$

Simplify the left side.

Simplify $2 (8 - 2 y) + y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 8 + 2 (- 2 y) + y = 7$

$x = 8 - 2 y$

Multiply $2$ by $8$ .

$16 + 2 (- 2 y) + y = 7$

$x = 8 - 2 y$

Multiply $- 2$ by $2$ .

$16 - 4 y + y = 7$

$x = 8 - 2 y$

$16 - 4 y + y = 7$

$x = 8 - 2 y$

Add $- 4 y$ and $y$ .

$16 - 3 y = 7$

$x = 8 - 2 y$

$16 - 3 y = 7$

$x = 8 - 2 y$

$16 - 3 y = 7$

$x = 8 - 2 y$

$16 - 3 y = 7$

$x = 8 - 2 y$

Step 3

Solve for $y$ in $16 - 3 y = 7$ .

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

Subtract $16$ from both sides of the equation.

$- 3 y = 7 - 16$

$x = 8 - 2 y$

Subtract $16$ from $7$ .

$- 3 y = - 9$

$x = 8 - 2 y$

$- 3 y = - 9$

$x = 8 - 2 y$

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

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

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

$x = 8 - 2 y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$x = 8 - 2 y$

Divide $y$ by $1$ .

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

$x = 8 - 2 y$

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

$x = 8 - 2 y$

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

$x = 8 - 2 y$

Simplify the right side.

Divide $- 9$ by $- 3$ .

$y = 3$

$x = 8 - 2 y$

$y = 3$

$x = 8 - 2 y$

$y = 3$

$x = 8 - 2 y$

$y = 3$

$x = 8 - 2 y$

Step 4

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

Replace all occurrences of $y$ in $x = 8 - 2 y$ with $3$ .

$x = 8 - 2 \cdot 3$

$y = 3$

Simplify the right side.

Simplify $8 - 2 \cdot 3$ .

Multiply $- 2$ by $3$ .

$x = 8 - 6$

$y = 3$

Subtract $6$ from $8$ .

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

$x = 2$

$y = 3$

Step 5

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

$(2, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 3)$

Equation Form:

$x = 2, y = 3$

Step 7

Solve by Substitution x+2y=8 2x+y=7

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