Solve the System of Equations 2x-3y=2 x=6y-5

$2 x - 3 y = 2$ $x = 6 y - 5$

Step 1

Replace all occurrences of $x$ with $6 y - 5$ in each equation.

Replace all occurrences of $x$ in $2 x - 3 y = 2$ with $6 y - 5$ .

$2 (6 y - 5) - 3 y = 2$

$x = 6 y - 5$

Simplify the left side.

Simplify $2 (6 y - 5) - 3 y$ .

Simplify each term.

Apply the distributive property.

$2 (6 y) + 2 \cdot - 5 - 3 y = 2$

$x = 6 y - 5$

Multiply $6$ by $2$ .

$12 y + 2 \cdot - 5 - 3 y = 2$

$x = 6 y - 5$

Multiply $2$ by $- 5$ .

$12 y - 10 - 3 y = 2$

$x = 6 y - 5$

$12 y - 10 - 3 y = 2$

$x = 6 y - 5$

Subtract $3 y$ from $12 y$ .

$9 y - 10 = 2$

$x = 6 y - 5$

$9 y - 10 = 2$

$x = 6 y - 5$

$9 y - 10 = 2$

$x = 6 y - 5$

$9 y - 10 = 2$

$x = 6 y - 5$

Step 2

Solve for $y$ in $9 y - 10 = 2$ .

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

Add $10$ to both sides of the equation.

$9 y = 2 + 10$

$x = 6 y - 5$

Add $2$ and $10$ .

$9 y = 12$

$x = 6 y - 5$

$9 y = 12$

$x = 6 y - 5$

Divide each term in $9 y = 12$ by $9$ and simplify.

Divide each term in $9 y = 12$ by $9$ .

$\frac{9 y}{9} = \frac{12}{9}$

$x = 6 y - 5$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{12}{9}$

$x = 6 y - 5$

Divide $y$ by $1$ .

$y = \frac{12}{9}$

$x = 6 y - 5$

$y = \frac{12}{9}$

$x = 6 y - 5$

$y = \frac{12}{9}$

$x = 6 y - 5$

Simplify the right side.

Cancel the common factor of $12$ and $9$ .

Factor $3$ out of $12$ .

$y = \frac{3 (4)}{9}$

$x = 6 y - 5$

Cancel the common factors.

Factor $3$ out of $9$ .

$y = \frac{3 \cdot 4}{3 \cdot 3}$

$x = 6 y - 5$

Cancel the common factor.

$y = \frac{3 \cdot 4}{3 \cdot 3}$

$x = 6 y - 5$

Rewrite the expression.

$y = \frac{4}{3}$

$x = 6 y - 5$

$y = \frac{4}{3}$

$x = 6 y - 5$

$y = \frac{4}{3}$

$x = 6 y - 5$

$y = \frac{4}{3}$

$x = 6 y - 5$

$y = \frac{4}{3}$

$x = 6 y - 5$

$y = \frac{4}{3}$

$x = 6 y - 5$

Step 3

Replace all occurrences of $y$ with $\frac{4}{3}$ in each equation.

Replace all occurrences of $y$ in $x = 6 y - 5$ with $\frac{4}{3}$ .

$x = 6 (\frac{4}{3}) - 5$

$y = \frac{4}{3}$

Simplify the right side.

Simplify $6 (\frac{4}{3}) - 5$ .

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$x = 3 (2) (\frac{4}{3}) - 5$

$y = \frac{4}{3}$

Cancel the common factor.

$x = 3 \cdot (2 (\frac{4}{3})) - 5$

$y = \frac{4}{3}$

Rewrite the expression.

$x = 2 \cdot 4 - 5$

$y = \frac{4}{3}$

$x = 2 \cdot 4 - 5$

$y = \frac{4}{3}$

Multiply $2$ by $4$ .

$x = 8 - 5$

$y = \frac{4}{3}$

$x = 8 - 5$

$y = \frac{4}{3}$

Subtract $5$ from $8$ .

$x = 3$

$y = \frac{4}{3}$

$x = 3$

$y = \frac{4}{3}$

$x = 3$

$y = \frac{4}{3}$

$x = 3$

$y = \frac{4}{3}$

Step 4

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

$(3, \frac{4}{3})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, \frac{4}{3})$

Equation Form:

$x = 3, y = \frac{4}{3}$

Step 6

Solve the System of Equations 2x-3y=2 x=6y-5

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