Question

Write one value of a for which the equations of the following system are
inconsistent:
2x+y=a
4x =7-2y

Answer 1

let us write the two equations in slope-intercept form:
\[
y=-2x+a\qquad\ldots(1)\\
2y=-4x+7\implies y=-2x+{7\over2}\qquad\ldots(2)
\]
now, two equations are inconsistent when their slopes are equal

what are the slopes of these two lines?

Answer 2

-2x?

Answer 3

just the "-2" part.

Answer 4

since the slopes are equal, it does not matter what value you choose for "a"; they'd always be in-consistent

Answer 5

it can be anything besides 7/2 right?

Answer 6

it can even be 7/2
no limitation
cannot be infinite o'course.

Answer 7

but if it would be 7/2 wouldn't it be consistent?

Answer 8

how?
the definition for in-consistency only deals with the slope.
well, if you had a=7/2, then the two lines would be identical. Even then they are inconsistent. But depends on how your teacher taught it. Technically, "a" can be any finite real number.

Answer 9

oh okay thank you.

Answer 10

yw