Here's a riddle??

Question

y = 2x + 1 (eq of a line)
y = 2x + 2 (eq of a line)
Therefore , 2x + 1 = 2x + 2
therefore 1 = 2
This is not true. why????

well if you find the intersection of 2 lines then y has one and the same value for the 2 eq so technically you can have 2x +1 = 2x +2

there's a catch in this riddle... you gotta spot it and explain it

Answer 1

As explained in previous answers, the two equations each represent two different lines. However, from your comment, I think you're not asking why "1 = 2." I think you're asking why it is impossible to find the intersections of these two lines.

Both lines have the same slope, but one intersects the "y-axis" at y=2 and the other at y=1. This means that they're parallel and different. Thus, the two lines never intersect.

If one of the lines had a different slope, for example:

y1 = 2x + 1
y2 = 3x + 2

Then you could solve for their intersection:

2x + 1 = 3x + 2
2x = 3x + 1
-x = 1
x = -1

In this NEW case, they intersect at (x, y)=(-1, -1). Their intersection is driven by the fact that they have different SLOPES.

Answer 2

You have 2 parallel lines (lines on a plane that never intersect), so if you try to solve for their intersection by equating them, you will arrive at a no solution for x. Or is there?
y = 2x + 1
y = 2x + 2

So you equate them
2x + 1 = 2x + 2

Thus,
2x - 2x = 2 - 1

And
x(2 - 2) = 1

Since 2 - 2 = 0, then
x · 0 = 1

We divide both equations by 0:
x · 0/0 = 1/0

We know that 0/0 = any real number (Let it be R), and 1/0 = +∞ (positive infinity), so
x · R = +∞

Now there are 2 cases for R: R is zero or R is not zero. If R is zero, then it reduces to
x · 0 = +∞

We again divide both sides by 0:
x · 0/0 = +∞/0

The right side is again +∞, and 0/0 is again R.
x · R = +∞

We notice that it is the same case, where R can be 0 or not 0. Now we try the case when R is not zero. Now we can divide both sides by R.
x · R/R = +∞/R

Now, R/R = 1 and R can be + or -, so the right side can be +∞ or -∞.
x = ±∞

Thus, these parallel lines intersect at +∞ or -∞.

^_^

Answer 3

You cannot simply add two equations together. You need to substitute a variable first.

let x=1

eq1. y = 2x + 1 => y = 3
eq2. y = 2x + 2 => y = 4


This actualy says nothing, other than y not being equal to y. If you were asked to solve the two equations, you'd need to make both equations equal first.

eq1. 2x + 1 - y = 0
eq2. 2x + 2 - y = 0

Since 0 = 0 {you can't use "y = y" since y is a variable. 0 is always the same} you can say:
2x + 1 - y = 2x + 2 - y

Answer 4

Actually, all you're doing is establishing that the two lines don't intersect -- that there is no single pair of numbers, (x,y), which makes both equations true. Specifically, the assumption that y in one equation can equal y in the other creates a contradiction (1=2). And, in fact, the two lines have the same slope (2) but different y-intercepts ( (0,1) and (0,2) respectively), which means they're parallel and non-coincident, so they really do never intersect.

Answer 5

Contrary to what most people are saying you could normally do this as long as the lines meet.
However these lines are parallel, so they never meet. That's why you get the impossible situation.

You have 2 linear simultaneous equations here. Such equations can have one solution for x and one for y if the lines intersect, no solutions if the lines are parallel as here or infinitely many solutions if the lines are the same such as y=2x + 1 and 2y=4x + 2.

Answer 6

Others have given you the correct answer but I must save you from chafer17.

2x + 1 and 2x + 2 divided through by 2 gives

x +1/2 and x + 1

Answer 7

When we equate the values of y in the two equations, we assume that the two lines intersect and there is a value of y (also x) which satisfies both the equations. When we proceed by equating the two values of y, we reach the conclusion that 1=2, which is not true. Therefore, our hypothesis that the two lines intersect is nullified.

Answer 8

If you are a "beginner" in this... you should not find this context in the same exercise...(otherwise the book you have is not correctly edited for you level). In the same exercise you should have there y1=2x+1 and y2=2x+2. y is an "abreviation" for function... More corectly whould of been f(x)=2x+1 and g(x)=2x+2... In this way you could see the difference...

Answer 9

You have the equation of two lines which never intersect. You can only put two equations equal to one another and come up with a sensible answer for x and y if the two lines intersect.

Answer 10

well, you have given eqn. of two different lines.
this means it is y1=2x+1 and y2=2x+2
you can compare them only to find intersection of the two
lines.
when comparing you are finding values of x and y which are common to both eqns.
so, what you said is not true