Question

An equation is shown below:

7x + y = 5

Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent.

Answer 1

assume an equation in the form:
ax + by = c
7x + y = 5

this system can be represented like:
\[\left[\begin{matrix}7 & 1 \\ a & b\end{matrix}\right] \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}5 \\ c\end{matrix}\right)\]

Answer 2

find the determinant of first matrix
\[\det \left( \left[\begin{matrix}7 & 1 \\ a & b\end{matrix}\right] \right) = 7b - a = 0\]

Answer 3

o.o I havent learned that yet

Answer 4

It's cramer's rule

Answer 5

haven't you seen this?

Answer 6

um i dont think so...

Answer 7

Ok, there's another way to solve it

Answer 8

we have this equation:
7x + y = 5
y = -7x + 5
so it's slope is -7

Answer 9

we want to find another equation so that the system is inconsistent

Answer 10

grafically, this two equations do not touch each other, i.e. they are parallel not coincident

Answer 11

now that we know that, another equation that we can choose is in this form:
y = -7x + k, where k is any number you want, but 5

Answer 12

let's choose k = 0

Answer 13

then the system:
7x + y = 5
7x + y = 0
is a inconsistent system

Answer 14

got it?

Answer 15

thx i was offline sorry

Answer 16

lmao math -.- throwing cramers rule at a 9th grader

Answer 17

xD

Answer 18

hahahah