Question

How many solutions does the following system of equations have?

2y=5x+4
y=3x+2

a) infinitely many
b) zero
c) one
d) two

Answer 1

this is two equations of two different lines
IF they are the same line THEN they will have INFINITE solutions
IF they are NOT the same line but have the SAME slope, then there are NO solutions
IF they have different slopes then there is ONE solution

so lets get them to look more like the equations of a line we are used to y = mx+b
one is already in that form y = 3x+2
the other one 2y=5x+4
divide every term by 2
y = (5/2) x + 4

so we have two different lines with NON equal slopes

what is the answer?

Answer 2

Then, there would be one solution?

Answer 3

yes

Answer 4

correct

Answer 5

2 will never be the answer....

Answer 6

@zzr0ck3r \(x^2+3x+2=0\) how many solutions?

Answer 7

9-4*2>0 so 2

Answer 8

this is not two equations of lines though

Answer 9

i love this xD http://screencast.com/t/jz087EjjYt

Answer 10

two lines can never cross each other exactly twice in Euclid space

Answer 11

a curve is a line

Answer 12

semantics,
linear or affine

Answer 13

never mind i'll stop making fun of you xD

Answer 14

when someone says an equation of a line, they are talking about an affine function:)

Answer 15

also
y = mx+b is only linear if b = 0
so
y = 3x+3 is not a linear equation despite what everyone thinks

Answer 16

only y = mx is linear

Answer 17

in other words....every linear equation goes through the origin in R^2