Answer:
35
Step-by-step explanation:
The equations will be "consistent" when they describe lines that are not parallel.
<h3>Slopes</h3>
The slope of a line whose equation is written in this form is the opposite of the ratio of the y-coefficient to the x-coefficient:
line 1 slope = -8/20 = -2/5
line 2 slope = -14/35 = -2/5
These lines have the same slope, so will be parallel unless they have the same y-intercept.
<h3>Y-intercept</h3>
The y-intercept of each line is the ratio of the constant to the y-coefficient:
line 1 y-intercept = 20/20 = 1
line 2 y-intercept = k/35
We want these lines to have the same y-intercept so that they are not inconsistent. This requires ...
k/35 = 1
k = 35
For the equations to be consistent, we must have k = 35.
__
<em>Additional comment</em>
Linear equations are generally categorized as "consistent" or "inconsistent," and "dependent" or "independent."
Equations are "inconsistent" if there are no values of the variables that satisfy all of the equations. They are "dependent" if they describe exactly the same relation between the variables. "Consistent" equations may be "dependent" (describing the same line, as here), or "independent" (describing lines with different slopes.)
