Find the Points of Intersection y=2x+9 y=6-x

$y = 2 x + 9$ $y = 6 - x$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x + 9 = 6 - x$

Step 2

Solve $2 x + 9 = 6 - x$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$2 x + 9 + x = 6$

Add $2 x$ and $x$ .

$3 x + 9 = 6$

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

Subtract $9$ from both sides of the equation.

$3 x = 6 - 9$

Subtract $9$ from $6$ .

$3 x = - 3$

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

Divide each term in $3 x = - 3$ by $3$ .

$\frac{3 x}{3} = \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 3}{3}$

Divide $x$ by $1$ .

$x = \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$x = - 1$

Step 3

Evaluate $y$ when $x = - 1$ .

Substitute $- 1$ for $x$ .

$y = 6 - (- 1)$

Simplify $6 - (- 1)$ .

Multiply $- 1$ by $- 1$ .

$y = 6 + 1$

Add $6$ and $1$ .

$y = 7$

Step 4

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

$(- 1, 7)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 1, 7)$

Equation Form:

$x = - 1, y = 7$

Step 6

Find the Points of Intersection y=2x+9 y=6-x

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