Solve by Graphing -2x+y=7 , 3y=6x+4

$- 2 x + y = 7$ , $3 y = 6 x + 4$

Step 1

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

$y = 7 + 2 x$

$3 y = 6 x + 4$

Step 2

Divide each term in $3 y = 6 x + 4$ by $3$ and simplify.

Divide each term in $3 y = 6 x + 4$ by $3$ .

$\frac{3 y}{3} = \frac{6 x}{3} + \frac{4}{3}$

$y = 7 + 2 x$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6 x}{3} + \frac{4}{3}$

$y = 7 + 2 x$

Divide $y$ by $1$ .

$y = \frac{6 x}{3} + \frac{4}{3}$

$y = 7 + 2 x$

$y = \frac{6 x}{3} + \frac{4}{3}$

$y = 7 + 2 x$

$y = \frac{6 x}{3} + \frac{4}{3}$

$y = 7 + 2 x$

Simplify the right side.

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 x$ .

$y = \frac{3 (2 x)}{3} + \frac{4}{3}$

$y = 7 + 2 x$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = \frac{3 (2 x)}{3 (1)} + \frac{4}{3}$

$y = 7 + 2 x$

Cancel the common factor.

$y = \frac{3 (2 x)}{3 \cdot 1} + \frac{4}{3}$

$y = 7 + 2 x$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{4}{3}$

$y = 7 + 2 x$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{4}{3}$

$y = 7 + 2 x$

$y = 2 x + \frac{4}{3}$

$y = 7 + 2 x$

$y = 2 x + \frac{4}{3}$

$y = 7 + 2 x$

$y = 2 x + \frac{4}{3}$

$y = 7 + 2 x$

$y = 2 x + \frac{4}{3}$

$y = 7 + 2 x$

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=7 , 3y=6x+4

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