Solve by Graphing 2x+y=4 , 5y=10x+4

$2 x + y = 4$ , $5 y = 10 x + 4$

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 4 - 2 x$

$5 y = 10 x + 4$

Step 2

Divide each term in $5 y = 10 x + 4$ by $5$ and simplify.

Divide each term in $5 y = 10 x + 4$ by $5$ .

$\frac{5 y}{5} = \frac{10 x}{5} + \frac{4}{5}$

$y = 4 - 2 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{10 x}{5} + \frac{4}{5}$

$y = 4 - 2 x$

Divide $y$ by $1$ .

$y = \frac{10 x}{5} + \frac{4}{5}$

$y = 4 - 2 x$

$y = \frac{10 x}{5} + \frac{4}{5}$

$y = 4 - 2 x$

$y = \frac{10 x}{5} + \frac{4}{5}$

$y = 4 - 2 x$

Simplify the right side.

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

Factor $5$ out of $10 x$ .

$y = \frac{5 (2 x)}{5} + \frac{4}{5}$

$y = 4 - 2 x$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = \frac{5 (2 x)}{5 (1)} + \frac{4}{5}$

$y = 4 - 2 x$

Cancel the common factor.

$y = \frac{5 (2 x)}{5 \cdot 1} + \frac{4}{5}$

$y = 4 - 2 x$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{4}{5}$

$y = 4 - 2 x$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{4}{5}$

$y = 4 - 2 x$

$y = 2 x + \frac{4}{5}$

$y = 4 - 2 x$

$y = 2 x + \frac{4}{5}$

$y = 4 - 2 x$

$y = 2 x + \frac{4}{5}$

$y = 4 - 2 x$

$y = 2 x + \frac{4}{5}$

$y = 4 - 2 x$

Step 3

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

$(\frac{4}{5}, \frac{12}{5})$

Step 4

Solve by Graphing 2x+y=4 , 5y=10x+4

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