Find the Points of Intersection x+4y=5 3x-4y=17

$x + 4 y = 5$ $3 x - 4 y = 17$

Subtract $4 y$ from both sides of the equation.

$x = 5 - 4 y$

$3 x - 4 y = 17$

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

Replace all occurrences of $x$ in $3 x - 4 y = 17$ with $5 - 4 y$ .

$3 (5 - 4 y) - 4 y = 17$

$x = 5 - 4 y$

Simplify the left side.

Simplify $3 (5 - 4 y) - 4 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 5 + 3 (- 4 y) - 4 y = 17$

$x = 5 - 4 y$

Multiply $3$ by $5$ .

$15 + 3 (- 4 y) - 4 y = 17$

$x = 5 - 4 y$

Multiply $- 4$ by $3$ .

$15 - 12 y - 4 y = 17$

$x = 5 - 4 y$

$15 - 12 y - 4 y = 17$

$x = 5 - 4 y$

Subtract $4 y$ from $- 12 y$ .

$15 - 16 y = 17$

$x = 5 - 4 y$

$15 - 16 y = 17$

$x = 5 - 4 y$

$15 - 16 y = 17$

$x = 5 - 4 y$

$15 - 16 y = 17$

$x = 5 - 4 y$

Solve for $y$ in $15 - 16 y = 17$ .

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

Subtract $15$ from both sides of the equation.

$- 16 y = 17 - 15$

$x = 5 - 4 y$

Subtract $15$ from $17$ .

$- 16 y = 2$

$x = 5 - 4 y$

$- 16 y = 2$

$x = 5 - 4 y$

Divide each term in $- 16 y = 2$ by $- 16$ and simplify.

Divide each term in $- 16 y = 2$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{2}{- 16}$

$x = 5 - 4 y$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{2}{- 16}$

$x = 5 - 4 y$

Divide $y$ by $1$ .

$y = \frac{2}{- 16}$

$x = 5 - 4 y$

$y = \frac{2}{- 16}$

$x = 5 - 4 y$

$y = \frac{2}{- 16}$

$x = 5 - 4 y$

Simplify the right side.

Cancel the common factor of $2$ and $- 16$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 16}$

$x = 5 - 4 y$

Cancel the common factors.

Factor $2$ out of $- 16$ .

$y = \frac{2 \cdot 1}{2 \cdot - 8}$

$x = 5 - 4 y$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 8}$

$x = 5 - 4 y$

Rewrite the expression.

$y = \frac{1}{- 8}$

$x = 5 - 4 y$

$y = \frac{1}{- 8}$

$x = 5 - 4 y$

$y = \frac{1}{- 8}$

$x = 5 - 4 y$

Move the negative in front of the fraction.

$y = - \frac{1}{8}$

$x = 5 - 4 y$

$y = - \frac{1}{8}$

$x = 5 - 4 y$

$y = - \frac{1}{8}$

$x = 5 - 4 y$

$y = - \frac{1}{8}$

$x = 5 - 4 y$

Replace all occurrences of $y$ with $- \frac{1}{8}$ in each equation.

Replace all occurrences of $y$ in $x = 5 - 4 y$ with $- \frac{1}{8}$ .

$x = 5 - 4 (- \frac{1}{8})$

$y = - \frac{1}{8}$

Simplify the right side.

Simplify $5 - 4 (- \frac{1}{8})$ .

Simplify each term.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$x = 5 - 4 (\frac{- 1}{8})$

$y = - \frac{1}{8}$

Factor $4$ out of $- 4$ .

$x = 5 + 4 (- 1) (\frac{- 1}{8})$

$y = - \frac{1}{8}$

Factor $4$ out of $8$ .

$x = 5 + 4 \cdot (- 1 \frac{- 1}{4 \cdot 2})$

$y = - \frac{1}{8}$

Cancel the common factor.

$x = 5 + 4 \cdot (- 1 \frac{- 1}{4 \cdot 2})$

$y = - \frac{1}{8}$

Rewrite the expression.

$x = 5 - 1 (\frac{- 1}{2})$

$y = - \frac{1}{8}$

$x = 5 - 1 (\frac{- 1}{2})$

$y = - \frac{1}{8}$

Move the negative in front of the fraction.

$x = 5 - 1 (- \frac{1}{2})$

$y = - \frac{1}{8}$

Multiply $- 1 (- \frac{1}{2})$ .

Multiply $- 1$ by $- 1$ .

$x = 5 + 1 (\frac{1}{2})$

$y = - \frac{1}{8}$

Multiply $\frac{1}{2}$ by $1$ .

$x = 5 + \frac{1}{2}$

$y = - \frac{1}{8}$

$x = 5 + \frac{1}{2}$

$y = - \frac{1}{8}$

$x = 5 + \frac{1}{2}$

$y = - \frac{1}{8}$

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = 5 \cdot \frac{2}{2} + \frac{1}{2}$

$y = - \frac{1}{8}$

Combine $5$ and $\frac{2}{2}$ .

$x = \frac{5 \cdot 2}{2} + \frac{1}{2}$

$y = - \frac{1}{8}$

Combine the numerators over the common denominator.

$x = \frac{5 \cdot 2 + 1}{2}$

$y = - \frac{1}{8}$

Simplify the numerator.

Multiply $5$ by $2$ .

$x = \frac{10 + 1}{2}$

$y = - \frac{1}{8}$

Add $10$ and $1$ .

$x = \frac{11}{2}$

$y = - \frac{1}{8}$

$x = \frac{11}{2}$

$y = - \frac{1}{8}$

$x = \frac{11}{2}$

$y = - \frac{1}{8}$

$x = \frac{11}{2}$

$y = - \frac{1}{8}$

$x = \frac{11}{2}$

$y = - \frac{1}{8}$

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

$(\frac{11}{2}, - \frac{1}{8})$

The result can be shown in multiple forms.

Point Form:

$(\frac{11}{2}, - \frac{1}{8})$

Equation Form:

$x = \frac{11}{2}, y = - \frac{1}{8}$

Find the Points of Intersection x+4y=5 3x-4y=17

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