Final answer:
The two linear equations share the property that they are both straight lines, can be expressed in slope-intercept form, and have y as the dependent variable and x as the independent variable. They have different slopes and y-intercepts, indicating that they are not parallel and will intersect at a single point.
Step-by-step explanation:
Two linear equations 7y = 3x - 14 and -4y + x = 8 share some common characteristics. Both equations represent straight lines, and they can be expressed in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To find their commonalities, we can manipulate each equation to express it in this standard form.
For the first equation, by dividing both sides by 7, we get y = (3/7)x - 2. For the second equation, we can rearrange it to y = (1/4)x - 2. Both equations now clearly show that y is the dependent variable that changes based on the value of x, the independent variable.
The most important thing they have in common is that they could potentially intersect, as they are not parallel (since their slopes are not equal), and they are not the same line (they have different y-intercepts). This means that these two lines will cross at a point which will be the solution to the system of equations, defining a specific x and y that satisfies both equations.