Solve by Substitution 5x-6=y 2x-3y=4

$5 x - 6 = y$ $2 x - 3 y = 4$

Step 1

Rewrite the equation as $y = 5 x - 6$ .

$y = 5 x - 6$

$2 x - 3 y = 4$

Step 2

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

Replace all occurrences of $y$ in $2 x - 3 y = 4$ with $5 x - 6$ .

$2 x - 3 (5 x - 6) = 4$

$y = 5 x - 6$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$2 x - 3 (5 x) - 3 \cdot - 6 = 4$

$y = 5 x - 6$

Multiply $5$ by $- 3$ .

$2 x - 15 x - 3 \cdot - 6 = 4$

$y = 5 x - 6$

Multiply $- 3$ by $- 6$ .

$2 x - 15 x + 18 = 4$

$y = 5 x - 6$

$2 x - 15 x + 18 = 4$

$y = 5 x - 6$

Subtract $15 x$ from $2 x$ .

$- 13 x + 18 = 4$

$y = 5 x - 6$

$- 13 x + 18 = 4$

$y = 5 x - 6$

$- 13 x + 18 = 4$

$y = 5 x - 6$

$- 13 x + 18 = 4$

$y = 5 x - 6$

Step 3

Solve for $x$ in $- 13 x + 18 = 4$ .

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

Subtract $18$ from both sides of the equation.

$- 13 x = 4 - 18$

$y = 5 x - 6$

Subtract $18$ from $4$ .

$- 13 x = - 14$

$y = 5 x - 6$

$- 13 x = - 14$

$y = 5 x - 6$

Divide each term in $- 13 x = - 14$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 14$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 14}{- 13}$

$y = 5 x - 6$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 14}{- 13}$

$y = 5 x - 6$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 13}$

$y = 5 x - 6$

$x = \frac{- 14}{- 13}$

$y = 5 x - 6$

$x = \frac{- 14}{- 13}$

$y = 5 x - 6$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{14}{13}$

$y = 5 x - 6$

$x = \frac{14}{13}$

$y = 5 x - 6$

$x = \frac{14}{13}$

$y = 5 x - 6$

$x = \frac{14}{13}$

$y = 5 x - 6$

Step 4

Replace all occurrences of $x$ with $\frac{14}{13}$ in each equation.

Replace all occurrences of $x$ in $y = 5 x - 6$ with $\frac{14}{13}$ .

$y = 5 (\frac{14}{13}) - 6$

$x = \frac{14}{13}$

Simplify the right side.

Simplify $5 (\frac{14}{13}) - 6$ .

Multiply $5 (\frac{14}{13})$ .

Combine $5$ and $\frac{14}{13}$ .

$y = \frac{5 \cdot 14}{13} - 6$

$x = \frac{14}{13}$

Multiply $5$ by $14$ .

$y = \frac{70}{13} - 6$

$x = \frac{14}{13}$

$y = \frac{70}{13} - 6$

$x = \frac{14}{13}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$y = \frac{70}{13} - 6 \cdot \frac{13}{13}$

$x = \frac{14}{13}$

Combine $- 6$ and $\frac{13}{13}$ .

$y = \frac{70}{13} + \frac{- 6 \cdot 13}{13}$

$x = \frac{14}{13}$

Combine the numerators over the common denominator.

$y = \frac{70 - 6 \cdot 13}{13}$

$x = \frac{14}{13}$

Simplify the numerator.

Multiply $- 6$ by $13$ .

$y = \frac{70 - 78}{13}$

$x = \frac{14}{13}$

Subtract $78$ from $70$ .

$y = \frac{- 8}{13}$

$x = \frac{14}{13}$

$y = \frac{- 8}{13}$

$x = \frac{14}{13}$

Move the negative in front of the fraction.

$y = - \frac{8}{13}$

$x = \frac{14}{13}$

$y = - \frac{8}{13}$

$x = \frac{14}{13}$

$y = - \frac{8}{13}$

$x = \frac{14}{13}$

$y = - \frac{8}{13}$

$x = \frac{14}{13}$

Step 5

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

$(\frac{14}{13}, - \frac{8}{13})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{14}{13}, - \frac{8}{13})$

Equation Form:

$x = \frac{14}{13}, y = - \frac{8}{13}$

Step 7

Solve by Substitution 5x-6=y 2x-3y=4

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