Identify the Graph for 3(2x-4y)=12 and (x+y)/3-y/3=7

To solve this problem, let's rewrite each equation in the slope-intercept form.

• Equation 1: $3(2x - 4y) = 12$

First, simplify this equation:

$6x - 12y = 12$

Dividing the entire equation by 6 gives:

$x - 2y = 2$

Rearranging this equation to solve for $y$:

$-2y = -x + 2$

$y = \frac{x}{2} - 1$

The slope of this line is $\frac{1}{2}$, and the y-intercept is $-1$.

• Equation 2: $\frac{x+y}{3} - \frac{y}{3} = 7$

Simplify this equation:

$\frac{x+y}{3} - \frac{y}{3} = 7$

This simplifies to:

$\frac{x}{3} = 7$

Multiply through by 3 to solve for $x$:

$x = 21$

Thus, $x = 21$ is a vertical line through $x = 21$.

Now, comparing against the choices, while analyzing the slopes and intercepts:

The correct graph corresponds to lines: $y = \frac{x}{2} - 1$ and $x = 21$.

In the provided options, Choice 1 matches this description, as it contains a line with slope $\frac{1}{2}$ and another vertical line.

Therefore, the graph corresponding to the given equations is Choice 1.