Determine if Linear (9x+y)/5+(7y)/2=10

$\frac{9 x + y}{5} + \frac{7 y}{2} = 10$

Step 1

Solve the equation for $y$ .

Simplify $\frac{9 x + y}{5} + \frac{7 y}{2}$ .

To write $\frac{9 x + y}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 x + y}{5} \cdot \frac{2}{2} + \frac{7 y}{2} = 10$

To write $\frac{7 y}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9 x + y}{5} \cdot \frac{2}{2} + \frac{7 y}{2} \cdot \frac{5}{5} = 10$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9 x + y}{5}$ by $\frac{2}{2}$ .

$\frac{(9 x + y) \cdot 2}{5 \cdot 2} + \frac{7 y}{2} \cdot \frac{5}{5} = 10$

Multiply $5$ by $2$ .

$\frac{(9 x + y) \cdot 2}{10} + \frac{7 y}{2} \cdot \frac{5}{5} = 10$

Multiply $\frac{7 y}{2}$ by $\frac{5}{5}$ .

$\frac{(9 x + y) \cdot 2}{10} + \frac{7 y \cdot 5}{2 \cdot 5} = 10$

Multiply $2$ by $5$ .

$\frac{(9 x + y) \cdot 2}{10} + \frac{7 y \cdot 5}{10} = 10$

Combine the numerators over the common denominator.

$\frac{(9 x + y) \cdot 2 + 7 y \cdot 5}{10} = 10$

Simplify the numerator.

Apply the distributive property.

$\frac{9 x \cdot 2 + y \cdot 2 + 7 y \cdot 5}{10} = 10$

Multiply $2$ by $9$ .

$\frac{18 x + y \cdot 2 + 7 y \cdot 5}{10} = 10$

Move $2$ to the left of $y$ .

$\frac{18 x + 2 \cdot y + 7 y \cdot 5}{10} = 10$

Multiply $5$ by $7$ .

$\frac{18 x + 2 y + 35 y}{10} = 10$

Add $2 y$ and $35 y$ .

$\frac{18 x + 37 y}{10} = 10$

Multiply both sides by $10$ .

$\frac{18 x + 37 y}{10} \cdot 10 = 10 \cdot 10$

Simplify.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{18 x + 37 y}{10} \cdot 10 = 10 \cdot 10$

Rewrite the expression.

$18 x + 37 y = 10 \cdot 10$

Simplify the right side.

Multiply $10$ by $10$ .

$18 x + 37 y = 100$

Solve for $y$ .

Subtract $18 x$ from both sides of the equation.

$37 y = 100 - 18 x$

Divide each term in $37 y = 100 - 18 x$ by $37$ and simplify.

Divide each term in $37 y = 100 - 18 x$ by $37$ .

$\frac{37 y}{37} = \frac{100}{37} + \frac{- 18 x}{37}$

Simplify the left side.

Cancel the common factor of $37$ .

Cancel the common factor.

$\frac{37 y}{37} = \frac{100}{37} + \frac{- 18 x}{37}$

Divide $y$ by $1$ .

$y = \frac{100}{37} + \frac{- 18 x}{37}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{100}{37} - \frac{18 x}{37}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear

Determine if Linear (9x+y)/5+(7y)/2=10

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