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

Question

Which graph corresponds to the following equations?

3(2x4y)=12 3(2x-4y)=12

x+y3y3=7 \frac{x+y}{3}-\frac{y}{3}=7

Video Solution

Step-by-Step Solution

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

  • Equation 1: 3(2x4y)=12 3(2x - 4y) = 12

First, simplify this equation:

6x12y=12 6x - 12y = 12

Dividing the entire equation by 6 gives:

x2y=2 x - 2y = 2

Rearranging this equation to solve for y y :

2y=x+2 -2y = -x + 2

y=x21 y = \frac{x}{2} - 1

The slope of this line is 12 \frac{1}{2} , and the y-intercept is 1-1.

  • Equation 2: x+y3y3=7 \frac{x+y}{3} - \frac{y}{3} = 7

Simplify this equation:

x+y3y3=7\frac{x+y}{3} - \frac{y}{3} = 7

This simplifies to:

x3=7\frac{x}{3} = 7

Multiply through by 3 to solve for x x :

x=21 x = 21

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

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

The correct graph corresponds to lines: y=x21 y = \frac{x}{2} - 1 and x=21 x = 21 .

In the provided options, Choice 1 matches this description, as it contains a line with slope 12\frac{1}{2} and another vertical line.

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

Answer