Solve the System of Equations 3x-2y-1=0 y=5x+4

$3 x - 2 y - 1 = 0$ $y = 5 x + 4$

Replace all occurrences of $y$ with $5 x + 4$ in each equation.

Replace all occurrences of $y$ in $3 x - 2 y - 1 = 0$ with $5 x + 4$ .

$3 x - 2 (5 x + 4) - 1 = 0$

$y = 5 x + 4$

Simplify the left side.

Simplify $3 x - 2 (5 x + 4) - 1$ .

Simplify each term.

Apply the distributive property.

$3 x - 2 (5 x) - 2 \cdot 4 - 1 = 0$

$y = 5 x + 4$

Multiply $5$ by $- 2$ .

$3 x - 10 x - 2 \cdot 4 - 1 = 0$

$y = 5 x + 4$

Multiply $- 2$ by $4$ .

$3 x - 10 x - 8 - 1 = 0$

$y = 5 x + 4$

$3 x - 10 x - 8 - 1 = 0$

$y = 5 x + 4$

Simplify by adding terms.

Subtract $10 x$ from $3 x$ .

$- 7 x - 8 - 1 = 0$

$y = 5 x + 4$

Subtract $1$ from $- 8$ .

$- 7 x - 9 = 0$

$y = 5 x + 4$

$- 7 x - 9 = 0$

$y = 5 x + 4$

$- 7 x - 9 = 0$

$y = 5 x + 4$

$- 7 x - 9 = 0$

$y = 5 x + 4$

$- 7 x - 9 = 0$

$y = 5 x + 4$

Solve for $x$ in $- 7 x - 9 = 0$ .

Add $9$ to both sides of the equation.

$- 7 x = 9$

$y = 5 x + 4$

Divide each term in $- 7 x = 9$ by $- 7$ and simplify.

Divide each term in $- 7 x = 9$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{9}{- 7}$

$y = 5 x + 4$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{9}{- 7}$

$y = 5 x + 4$

Divide $x$ by $1$ .

$x = \frac{9}{- 7}$

$y = 5 x + 4$

$x = \frac{9}{- 7}$

$y = 5 x + 4$

$x = \frac{9}{- 7}$

$y = 5 x + 4$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{9}{7}$

$y = 5 x + 4$

$x = - \frac{9}{7}$

$y = 5 x + 4$

$x = - \frac{9}{7}$

$y = 5 x + 4$

$x = - \frac{9}{7}$

$y = 5 x + 4$

Replace all occurrences of $x$ with $- \frac{9}{7}$ in each equation.

Replace all occurrences of $x$ in $y = 5 x + 4$ with $- \frac{9}{7}$ .

$y = 5 (- \frac{9}{7}) + 4$

$x = - \frac{9}{7}$

Simplify the right side.

Simplify $5 (- \frac{9}{7}) + 4$ .

Simplify each term.

Multiply $5 (- \frac{9}{7})$ .

Multiply $- 1$ by $5$ .

$y = - 5 (\frac{9}{7}) + 4$

$x = - \frac{9}{7}$

Combine $- 5$ and $\frac{9}{7}$ .

$y = \frac{- 5 \cdot 9}{7} + 4$

$x = - \frac{9}{7}$

Multiply $- 5$ by $9$ .

$y = \frac{- 45}{7} + 4$

$x = - \frac{9}{7}$

$y = \frac{- 45}{7} + 4$

$x = - \frac{9}{7}$

Move the negative in front of the fraction.

$y = - \frac{45}{7} + 4$

$x = - \frac{9}{7}$

$y = - \frac{45}{7} + 4$

$x = - \frac{9}{7}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - \frac{45}{7} + 4 \cdot \frac{7}{7}$

$x = - \frac{9}{7}$

Combine $4$ and $\frac{7}{7}$ .

$y = - \frac{45}{7} + \frac{4 \cdot 7}{7}$

$x = - \frac{9}{7}$

Combine the numerators over the common denominator.

$y = \frac{- 45 + 4 \cdot 7}{7}$

$x = - \frac{9}{7}$

Simplify the numerator.

Multiply $4$ by $7$ .

$y = \frac{- 45 + 28}{7}$

$x = - \frac{9}{7}$

Add $- 45$ and $28$ .

$y = \frac{- 17}{7}$

$x = - \frac{9}{7}$

$y = \frac{- 17}{7}$

$x = - \frac{9}{7}$

Move the negative in front of the fraction.

$y = - \frac{17}{7}$

$x = - \frac{9}{7}$

$y = - \frac{17}{7}$

$x = - \frac{9}{7}$

$y = - \frac{17}{7}$

$x = - \frac{9}{7}$

$y = - \frac{17}{7}$

$x = - \frac{9}{7}$

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

$(- \frac{9}{7}, - \frac{17}{7})$

The result can be shown in multiple forms.

Point Form:

$(- \frac{9}{7}, - \frac{17}{7})$

Equation Form:

$x = - \frac{9}{7}, y = - \frac{17}{7}$

Solve the System of Equations 3x-2y-1=0 y=5x+4

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