Solve by Graphing -2x+y=3 , 5y=10x-15

$- 2 x + y = 3$ , $5 y = 10 x - 15$

Step 1

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

$y = 3 + 2 x$

$5 y = 10 x - 15$

Step 2

Divide each term in $5 y = 10 x - 15$ by $5$ and simplify.

Divide each term in $5 y = 10 x - 15$ by $5$ .

$\frac{5 y}{5} = \frac{10 x}{5} + \frac{- 15}{5}$

$y = 3 + 2 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{10 x}{5} + \frac{- 15}{5}$

$y = 3 + 2 x$

Divide $y$ by $1$ .

$y = \frac{10 x}{5} + \frac{- 15}{5}$

$y = 3 + 2 x$

$y = \frac{10 x}{5} + \frac{- 15}{5}$

$y = 3 + 2 x$

$y = \frac{10 x}{5} + \frac{- 15}{5}$

$y = 3 + 2 x$

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 x$ .

$y = \frac{5 (2 x)}{5} + \frac{- 15}{5}$

$y = 3 + 2 x$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = \frac{5 (2 x)}{5 (1)} + \frac{- 15}{5}$

$y = 3 + 2 x$

Cancel the common factor.

$y = \frac{5 (2 x)}{5 \cdot 1} + \frac{- 15}{5}$

$y = 3 + 2 x$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{- 15}{5}$

$y = 3 + 2 x$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{- 15}{5}$

$y = 3 + 2 x$

$y = 2 x + \frac{- 15}{5}$

$y = 3 + 2 x$

$y = 2 x + \frac{- 15}{5}$

$y = 3 + 2 x$

Divide $- 15$ by $5$ .

$y = 2 x - 3$

$y = 3 + 2 x$

$y = 2 x - 3$

$y = 3 + 2 x$

$y = 2 x - 3$

$y = 3 + 2 x$

$y = 2 x - 3$

$y = 3 + 2 x$

Step 3

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

No solution

Step 4

Solve by Graphing -2x+y=3 , 5y=10x-15

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