Find the Points of Intersection 16x-2y=74 2x-2y=4

$16 x - 2 y = 74$ $2 x - 2 y = 4$

Step 1

Solve for $x$ in $16 x - 2 y = 74$ .

Add $2 y$ to both sides of the equation.

$16 x = 74 + 2 y$

$2 x - 2 y = 4$

Divide each term in $16 x = 74 + 2 y$ by $16$ and simplify.

Divide each term in $16 x = 74 + 2 y$ by $16$ .

$\frac{16 x}{16} = \frac{74}{16} + \frac{2 y}{16}$

$2 x - 2 y = 4$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{74}{16} + \frac{2 y}{16}$

$2 x - 2 y = 4$

Divide $x$ by $1$ .

$x = \frac{74}{16} + \frac{2 y}{16}$

$2 x - 2 y = 4$

$x = \frac{74}{16} + \frac{2 y}{16}$

$2 x - 2 y = 4$

$x = \frac{74}{16} + \frac{2 y}{16}$

$2 x - 2 y = 4$

Simplify the right side.

Simplify each term.

Cancel the common factor of $74$ and $16$ .

Factor $2$ out of $74$ .

$x = \frac{2 (37)}{16} + \frac{2 y}{16}$

$2 x - 2 y = 4$

Cancel the common factors.

Factor $2$ out of $16$ .

$x = \frac{2 \cdot 37}{2 \cdot 8} + \frac{2 y}{16}$

$2 x - 2 y = 4$

Cancel the common factor.

$x = \frac{2 \cdot 37}{2 \cdot 8} + \frac{2 y}{16}$

$2 x - 2 y = 4$

Rewrite the expression.

$x = \frac{37}{8} + \frac{2 y}{16}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{2 y}{16}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{2 y}{16}$

$2 x - 2 y = 4$

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

Factor $2$ out of $2 y$ .

$x = \frac{37}{8} + \frac{2 (y)}{16}$

$2 x - 2 y = 4$

Cancel the common factors.

Factor $2$ out of $16$ .

$x = \frac{37}{8} + \frac{2 y}{2 \cdot 8}$

$2 x - 2 y = 4$

Cancel the common factor.

$x = \frac{37}{8} + \frac{2 y}{2 \cdot 8}$

$2 x - 2 y = 4$

Rewrite the expression.

$x = \frac{37}{8} + \frac{y}{8}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$2 x - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$2 x - 2 y = 4$

Step 2

Replace all occurrences of $x$ with $\frac{37}{8} + \frac{y}{8}$ in each equation.

Replace all occurrences of $x$ in $2 x - 2 y = 4$ with $\frac{37}{8} + \frac{y}{8}$ .

$2 (\frac{37}{8} + \frac{y}{8}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Simplify the left side.

Simplify $2 (\frac{37}{8} + \frac{y}{8}) - 2 y$ .

Simplify each term.

Apply the distributive property.

$2 (\frac{37}{8}) + 2 (\frac{y}{8}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$2 (\frac{37}{2 (4)}) + 2 (\frac{y}{8}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Cancel the common factor.

$2 (\frac{37}{2 \cdot 4}) + 2 (\frac{y}{8}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Rewrite the expression.

$\frac{37}{4} + 2 (\frac{y}{8}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$\frac{37}{4} + 2 (\frac{y}{8}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{37}{4} + 2 (\frac{y}{2 (4)}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Cancel the common factor.

$\frac{37}{4} + 2 (\frac{y}{2 \cdot 4}) - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Rewrite the expression.

$\frac{37}{4} + \frac{y}{4} - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$\frac{37}{4} + \frac{y}{4} - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$\frac{37}{4} + \frac{y}{4} - 2 y = 4$

$x = \frac{37}{8} + \frac{y}{8}$

To write $- 2 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{37}{4} + \frac{y}{4} - 2 y \cdot \frac{4}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Combine $- 2 y$ and $\frac{4}{4}$ .

$\frac{37}{4} + \frac{y}{4} + \frac{- 2 y \cdot 4}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Combine the numerators over the common denominator.

$\frac{37}{4} + \frac{y - 2 y \cdot 4}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Combine the numerators over the common denominator.

$\frac{37 + y - 2 y \cdot 4}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Multiply $4$ by $- 2$ .

$\frac{37 + y - 8 y}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Subtract $8 y$ from $y$ .

$\frac{37 - 7 y}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$\frac{37 - 7 y}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$\frac{37 - 7 y}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

$\frac{37 - 7 y}{4} = 4$

$x = \frac{37}{8} + \frac{y}{8}$

Step 3

Solve for $y$ in $\frac{37 - 7 y}{4} = 4$ .

Multiply both sides by $4$ .

$\frac{37 - 7 y}{4} \cdot 4 = 4 \cdot 4$

$x = \frac{37}{8} + \frac{y}{8}$

Simplify.

Simplify the left side.

Simplify $\frac{37 - 7 y}{4} \cdot 4$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{37 - 7 y}{4} \cdot 4 = 4 \cdot 4$

$x = \frac{37}{8} + \frac{y}{8}$

Rewrite the expression.

$37 - 7 y = 4 \cdot 4$

$x = \frac{37}{8} + \frac{y}{8}$

$37 - 7 y = 4 \cdot 4$

$x = \frac{37}{8} + \frac{y}{8}$

Reorder $37$ and $- 7 y$ .

$- 7 y + 37 = 4 \cdot 4$

$x = \frac{37}{8} + \frac{y}{8}$

$- 7 y + 37 = 4 \cdot 4$

$x = \frac{37}{8} + \frac{y}{8}$

$- 7 y + 37 = 4 \cdot 4$

$x = \frac{37}{8} + \frac{y}{8}$

Simplify the right side.

Multiply $4$ by $4$ .

$- 7 y + 37 = 16$

$x = \frac{37}{8} + \frac{y}{8}$

$- 7 y + 37 = 16$

$x = \frac{37}{8} + \frac{y}{8}$

$- 7 y + 37 = 16$

$x = \frac{37}{8} + \frac{y}{8}$

Solve for $y$ .

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

Subtract $37$ from both sides of the equation.

$- 7 y = 16 - 37$

$x = \frac{37}{8} + \frac{y}{8}$

Subtract $37$ from $16$ .

$- 7 y = - 21$

$x = \frac{37}{8} + \frac{y}{8}$

$- 7 y = - 21$

$x = \frac{37}{8} + \frac{y}{8}$

Divide each term in $- 7 y = - 21$ by $- 7$ and simplify.

Divide each term in $- 7 y = - 21$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 21}{- 7}$

$x = \frac{37}{8} + \frac{y}{8}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 21}{- 7}$

$x = \frac{37}{8} + \frac{y}{8}$

Divide $y$ by $1$ .

$y = \frac{- 21}{- 7}$

$x = \frac{37}{8} + \frac{y}{8}$

$y = \frac{- 21}{- 7}$

$x = \frac{37}{8} + \frac{y}{8}$

$y = \frac{- 21}{- 7}$

$x = \frac{37}{8} + \frac{y}{8}$

Simplify the right side.

Divide $- 21$ by $- 7$ .

$y = 3$

$x = \frac{37}{8} + \frac{y}{8}$

$y = 3$

$x = \frac{37}{8} + \frac{y}{8}$

$y = 3$

$x = \frac{37}{8} + \frac{y}{8}$

$y = 3$

$x = \frac{37}{8} + \frac{y}{8}$

$y = 3$

$x = \frac{37}{8} + \frac{y}{8}$

Step 4

Replace all occurrences of $y$ with $3$ in each equation.

Replace all occurrences of $y$ in $x = \frac{37}{8} + \frac{y}{8}$ with $3$ .

$x = \frac{37}{8} + \frac{3}{8}$

$y = 3$

Simplify the right side.

Simplify $\frac{37}{8} + \frac{3}{8}$ .

Combine the numerators over the common denominator.

$x = \frac{37 + 3}{8}$

$y = 3$

Simplify the expression.

Add $37$ and $3$ .

$x = \frac{40}{8}$

$y = 3$

Divide $40$ by $8$ .

$x = 5$

$y = 3$

$x = 5$

$y = 3$

$x = 5$

$y = 3$

$x = 5$

$y = 3$

$x = 5$

$y = 3$

Step 5

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

$(5, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 3)$

Equation Form:

$x = 5, y = 3$

Step 7

Find the Points of Intersection 16x-2y=74 2x-2y=4

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