Question

Solve the system
9=4x-2y
2x+6=y

Answer 1

Well for this one...you already know what y equals via that second equation

y = 2x + 6

so you can substitute that in for 'y' in the first equation

9 = 4x - 2y

9 = 4x - 2(2x + 6)

Now can you solve for 'x' ...?

Answer 2

no how do you solve for x?

Answer 3

We would simplify that equation

9 = 4x - 2(2x + 6)
9 = 4x - 4x - 12
9 = -12

there is no answer to this system of equations

Can anyone make sure I did that right? not too often is there no solution...

Answer 4

matrices says your right john!

Answer 5

I really should learn how to solve these via matrices...never learned that method

Thanks @chris00

Answer 6

well you can simply see that their is no solution by inspection!

Answer 7

the second equation is a scalar multiple of the first equation, however their constant's are not.

Answer 8

so since they are scalar multiples, then their can either be parallel and distinct ( don't lie on the same line) or they are parallel and coincident (they are vertually the same line...

Answer 9

since 6 Is not a scalar multiple of 9 in this case then the system is inconsistent based on the fact that these lines are parallel and distinct.