Solve the System of Equations 2x+3y=16.9 5x=y+7.4

$2 x + 3 y = 16.9$ $5 x = y + 7.4$

Step 1

Divide each term in $5 x = y + 7.4$ by $5$ and simplify.

Divide each term in $5 x = y + 7.4$ by $5$ .

$\frac{5 x}{5} = \frac{y}{5} + \frac{7.4}{5}$

$2 x + 3 y = 16.9$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{y}{5} + \frac{7.4}{5}$

$2 x + 3 y = 16.9$

Divide $x$ by $1$ .

$x = \frac{y}{5} + \frac{7.4}{5}$

$2 x + 3 y = 16.9$

$x = \frac{y}{5} + \frac{7.4}{5}$

$2 x + 3 y = 16.9$

$x = \frac{y}{5} + \frac{7.4}{5}$

$2 x + 3 y = 16.9$

Simplify the right side.

Divide $7.4$ by $5$ .

$x = \frac{y}{5} + 1.48$

$2 x + 3 y = 16.9$

$x = \frac{y}{5} + 1.48$

$2 x + 3 y = 16.9$

$x = \frac{y}{5} + 1.48$

$2 x + 3 y = 16.9$

Step 2

Replace all occurrences of $x$ with $\frac{y}{5} + 1.48$ in each equation.

Replace all occurrences of $x$ in $2 x + 3 y = 16.9$ with $\frac{y}{5} + 1.48$ .

$2 (\frac{y}{5} + 1.48) + 3 y = 16.9$

$x = \frac{y}{5} + 1.48$

Simplify the left side.

Simplify $2 (\frac{y}{5} + 1.48) + 3 y$ .

Simplify each term.

Apply the distributive property.

$2 (\frac{y}{5}) + 2 \cdot 1.48 + 3 y = 16.9$

$x = \frac{y}{5} + 1.48$

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

$\frac{2 y}{5} + 2 \cdot 1.48 + 3 y = 16.9$

$x = \frac{y}{5} + 1.48$

Multiply $2$ by $1.48$ .

$\frac{2 y}{5} + 2.96 + 3 y = 16.9$

$x = \frac{y}{5} + 1.48$

$\frac{2 y}{5} + 2.96 + 3 y = 16.9$

$x = \frac{y}{5} + 1.48$

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 y}{5} + 3 y \cdot \frac{5}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Simplify terms.

Combine $3 y$ and $\frac{5}{5}$ .

$\frac{2 y}{5} + \frac{3 y \cdot 5}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Combine the numerators over the common denominator.

$\frac{2 y + 3 y \cdot 5}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

$\frac{2 y + 3 y \cdot 5}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $2 y + 3 y \cdot 5$ .

Factor $y$ out of $2 y$ .

$\frac{y \cdot 2 + 3 y \cdot 5}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Factor $y$ out of $3 y \cdot 5$ .

$\frac{y \cdot 2 + y (3 \cdot 5)}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Factor $y$ out of $y \cdot 2 + y (3 \cdot 5)$ .

$\frac{y (2 + 3 \cdot 5)}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

$\frac{y (2 + 3 \cdot 5)}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Multiply $3$ by $5$ .

$\frac{y (2 + 15)}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Add $2$ and $15$ .

$\frac{y \cdot 17}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

$\frac{y \cdot 17}{5} + 2.96 = 16.9$

$x = \frac{y}{5} + 1.48$

Move $17$ to the left of $y$ .