Find the Points of Intersection x+y=8 and 2x-y=1

$x + y = 8$ and $2 x - y = 1$

Step 1

Subtract $y$ from both sides of the equation.

$x = 8 - y$

$2 x - y = 1$

Step 2

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

Replace all occurrences of $x$ in $2 x - y = 1$ with $8 - y$ .

$2 (8 - y) - y = 1$

$x = 8 - y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$2 \cdot 8 + 2 (- y) - y = 1$

$x = 8 - y$

Multiply $2$ by $8$ .

$16 + 2 (- y) - y = 1$

$x = 8 - y$

Multiply $- 1$ by $2$ .

$16 - 2 y - y = 1$

$x = 8 - y$

$16 - 2 y - y = 1$

$x = 8 - y$

Subtract $y$ from $- 2 y$ .

$16 - 3 y = 1$

$x = 8 - y$

$16 - 3 y = 1$

$x = 8 - y$

$16 - 3 y = 1$

$x = 8 - y$

$16 - 3 y = 1$

$x = 8 - y$

Step 3

Solve for $y$ in $16 - 3 y = 1$ .

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

Subtract $16$ from both sides of the equation.

$- 3 y = 1 - 16$

$x = 8 - y$

Subtract $16$ from $1$ .

$- 3 y = - 15$

$x = 8 - y$

$- 3 y = - 15$

$x = 8 - y$

Divide each term in $- 3 y = - 15$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 15$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3}$

$x = 8 - y$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3}$

$x = 8 - y$

Divide $y$ by $1$ .

$y = \frac{- 15}{- 3}$

$x = 8 - y$

$y = \frac{- 15}{- 3}$

$x = 8 - y$

$y = \frac{- 15}{- 3}$

$x = 8 - y$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$y = 5$

$x = 8 - y$

$y = 5$

$x = 8 - y$

$y = 5$

$x = 8 - y$

$y = 5$

$x = 8 - y$

Step 4

Replace all occurrences of $y$ with $5$ in each equation.

Replace all occurrences of $y$ in $x = 8 - y$ with $5$ .

$x = 8 - (5)$

$y = 5$

Simplify the right side.

Simplify $8 - (5)$ .

Multiply $- 1$ by $5$ .

$x = 8 - 5$

$y = 5$

Subtract $5$ from $8$ .

$x = 3$

$y = 5$

$x = 3$

$y = 5$

$x = 3$

$y = 5$

$x = 3$

$y = 5$

Step 5

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

$(3, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 5)$

Equation Form:

$x = 3, y = 5$

Step 7

Find the Points of Intersection x+y=8 and 2x-y=1

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