Final answer:
To determine which graph best represents the system of equations '2x = 6 - y' and '5x - 4y = 28', you must first convert both equations to slope-intercept form and then find the intersection point by setting the two equations equal to each other and solving for x and y.
Step-by-step explanation:
The system of equations contains two separate equations: 2x = 6 - y and 5x - 4y = 28. To graph these equations and find their solution, we need to rearrange each equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
For the first equation, 2x = 6 - y, we can rewrite it as y = -2x + 6. For the second equation, 5x - 4y = 28, we can rearrange it to y = (5/4)x - 7. The graphs of these two lines will intersect at the point that is the solution to the system of equations.
To find the intersection point, you could set the two equations equal to each other:
-2x + 6 = (5/4)x - 7. Solving for x gives you the x-coordinate of the intersection point. You would then substitute this x-value back into one of the original equations to get the y-coordinate for the intersection point.