Find the Points of Intersection 2x=3y-1 6x-9y=-3

$2 x = 3 y - 1$ $6 x - 9 y = - 3$

Step 1

Divide each term in $2 x = 3 y - 1$ by $2$ and simplify.

Divide each term in $2 x = 3 y - 1$ by $2$ .

$\frac{2 x}{2} = \frac{3 y}{2} + \frac{- 1}{2}$

$6 x - 9 y = - 3$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3 y}{2} + \frac{- 1}{2}$

$6 x - 9 y = - 3$

Divide $x$ by $1$ .

$x = \frac{3 y}{2} + \frac{- 1}{2}$

$6 x - 9 y = - 3$

$x = \frac{3 y}{2} + \frac{- 1}{2}$

$6 x - 9 y = - 3$

$x = \frac{3 y}{2} + \frac{- 1}{2}$

$6 x - 9 y = - 3$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{3 y}{2} - \frac{1}{2}$

$6 x - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$6 x - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$6 x - 9 y = - 3$

Step 2

Replace all occurrences of $x$ with $\frac{3 y}{2} - \frac{1}{2}$ in each equation.

Replace all occurrences of $x$ in $6 x - 9 y = - 3$ with $\frac{3 y}{2} - \frac{1}{2}$ .

$6 (\frac{3 y}{2} - \frac{1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Simplify the left side.

Simplify $6 (\frac{3 y}{2} - \frac{1}{2}) - 9 y$ .

Simplify each term.

Apply the distributive property.

$6 (\frac{3 y}{2}) + 6 (- \frac{1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 (3) (\frac{3 y}{2}) + 6 (- \frac{1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Cancel the common factor.

$2 \cdot (3 (\frac{3 y}{2})) + 6 (- \frac{1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Rewrite the expression.

$3 (3 y) + 6 (- \frac{1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$3 (3 y) + 6 (- \frac{1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Multiply $3$ by $3$ .

$9 y + 6 (- \frac{1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$9 y + 6 (\frac{- 1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Factor $2$ out of $6$ .

$9 y + 2 (3) (\frac{- 1}{2}) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Cancel the common factor.

$9 y + 2 \cdot (3 (\frac{- 1}{2})) - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Rewrite the expression.

$9 y + 3 \cdot - 1 - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$9 y + 3 \cdot - 1 - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Multiply $3$ by $- 1$ .

$9 y - 3 - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$9 y - 3 - 9 y = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Combine the opposite terms in $9 y - 3 - 9 y$ .

Subtract $9 y$ from $9 y$ .

$0 - 3 = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Subtract $3$ from $0$ .

$- 3 = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$- 3 = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$- 3 = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$- 3 = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

$- 3 = - 3$

$x = \frac{3 y}{2} - \frac{1}{2}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3 y}{2} - \frac{1}{2}$

Step 4

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