Solve by Graphing y=2/3x-5 4x-6y=30

$y = \frac{2}{3} x - 5$ $4 x - 6 y = 30$

Step 1

Combine $\frac{2}{3}$ and $x$ .

$y = \frac{2 x}{3} - 5$

$4 x - 6 y = 30$

Step 2

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

$- 6 y = 30 - 4 x$

$y = \frac{2 x}{3} - 5$

Step 3

Divide each term in $- 6 y = 30 - 4 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 30 - 4 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{30}{- 6} + \frac{- 4 x}{- 6}$

$y = \frac{2 x}{3} - 5$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{30}{- 6} + \frac{- 4 x}{- 6}$

$y = \frac{2 x}{3} - 5$

Divide $y$ by $1$ .

$y = \frac{30}{- 6} + \frac{- 4 x}{- 6}$

$y = \frac{2 x}{3} - 5$

$y = \frac{30}{- 6} + \frac{- 4 x}{- 6}$

$y = \frac{2 x}{3} - 5$

$y = \frac{30}{- 6} + \frac{- 4 x}{- 6}$

$y = \frac{2 x}{3} - 5$

Simplify the right side.

Simplify each term.

Divide $30$ by $- 6$ .

$y = - 5 + \frac{- 4 x}{- 6}$

$y = \frac{2 x}{3} - 5$

Cancel the common factor of $- 4$ and $- 6$ .

Factor $- 2$ out of $- 4 x$ .

$y = - 5 + \frac{- 2 (2 x)}{- 6}$

$y = \frac{2 x}{3} - 5$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$y = - 5 + \frac{- 2 (2 x)}{- 2 \cdot 3}$

$y = \frac{2 x}{3} - 5$

Cancel the common factor.

$y = - 5 + \frac{- 2 (2 x)}{- 2 \cdot 3}$

$y = \frac{2 x}{3} - 5$

Rewrite the expression.

$y = - 5 + \frac{2 x}{3}$

$y = \frac{2 x}{3} - 5$

$y = - 5 + \frac{2 x}{3}$

$y = \frac{2 x}{3} - 5$

$y = - 5 + \frac{2 x}{3}$

$y = \frac{2 x}{3} - 5$

$y = - 5 + \frac{2 x}{3}$

$y = \frac{2 x}{3} - 5$

$y = - 5 + \frac{2 x}{3}$

$y = \frac{2 x}{3} - 5$

$y = - 5 + \frac{2 x}{3}$

$y = \frac{2 x}{3} - 5$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

Always true

Step 5

Solve by Graphing y=2/3x-5 4x-6y=30

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