Solve by Substitution 6x-9=y and y=-3x

$6 x - 9 = y$ and $y = - 3 x$

Step 1

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

Replace all occurrences of $y$ in $6 x - 9 = y$ with $- 3 x$ .

$6 x - 9 = - 3 x$

$y = - 3 x$

Simplify the left side.

Remove parentheses.

$6 x - 9 = - 3 x$

$y = - 3 x$

$6 x - 9 = - 3 x$

$y = - 3 x$

$6 x - 9 = - 3 x$

$y = - 3 x$

Step 2

Solve for $x$ in $6 x - 9 = - 3 x$ .

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

Add $3 x$ to both sides of the equation.

$6 x - 9 + 3 x = 0$

$y = - 3 x$

Add $6 x$ and $3 x$ .

$9 x - 9 = 0$

$y = - 3 x$

$9 x - 9 = 0$

$y = - 3 x$

Add $9$ to both sides of the equation.

$9 x = 9$

$y = - 3 x$

Divide each term in $9 x = 9$ by $9$ and simplify.

Divide each term in $9 x = 9$ by $9$ .

$\frac{9 x}{9} = \frac{9}{9}$

$y = - 3 x$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{9}{9}$

$y = - 3 x$

Divide $x$ by $1$ .

$x = \frac{9}{9}$

$y = - 3 x$

$x = \frac{9}{9}$

$y = - 3 x$

$x = \frac{9}{9}$

$y = - 3 x$

Simplify the right side.

Divide $9$ by $9$ .

$x = 1$

$y = - 3 x$

$x = 1$

$y = - 3 x$

$x = 1$

$y = - 3 x$

$x = 1$

$y = - 3 x$

Step 3

Replace all occurrences of $x$ with $1$ in each equation.

Replace all occurrences of $x$ in $y = - 3 x$ with $1$ .

$y = - 3 \cdot 1$

$x = 1$

Simplify the right side.

Multiply $- 3$ by $1$ .

$y = - 3$

$x = 1$

$y = - 3$

$x = 1$

$y = - 3$

$x = 1$

Step 4

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

$(1, - 3)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, - 3)$

Equation Form:

$x = 1, y = - 3$

Step 6

Solve by Substitution 6x-9=y and y=-3x

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