Question

Two lines, A and B, are represented by the equations given below:

Line A: x + y = 2
Line B: 2x + y = 4

Which statement is true about the solution to the set of equations?



There are infinitely many solutions.
There are two solutions.
There is one solution.
There is no solution.

Answer 1

@Mehek14 plz show me how to do this???

Answer 2

hint:
please solve the first equation for \(y\)

Answer 3

? how do i solve it?

Answer 4

if I add \(-x\) to both sides, I get:
\(x-x+y=2-x\)
please simplify

Answer 5

what is \(x-x=...?\)

Answer 6

y

Answer 7

I think that:
\(x-x=0\), right?

Answer 8

oh yes i gues so

Answer 9

so, we can write:
\(y=2-x\)
am I right?

Answer 10

so there is one solution right?

Answer 11

please wait
next:
if I subtract \(2x\) from both sides of the \(second\) equation, I get:
\[\Large 2x - 2x + y = 4 - 2x\]
please simplify

Answer 12

what is \(2x-2x=...?\)

Answer 13

2x=4−y?

Answer 14

correct! :) nevertheless such equation is not useful. An equation which can be useful is:
\[\Large y = 4 - 2x\]

Answer 15

now, from first equation we got \(y=2-x\) whereas from second equation we got \(y=4-2x\), then we can write this:

\(\Large 2-x=4-2x\)

Answer 16

please solve that equation with respect to \(x\)

Answer 17

if we draw both of those lines, using the coordinates \((x,y)\), we get:

Answer 18

as we can see, we have only one intersection point, so what can you conclude?

Answer 19

that we got one solution

Answer 20

that's right!

Answer 21

thank you very much for explaining this whole thing to me @Michele_Laino it's very nice of you!!! :D

Answer 22

thanks!! :D

Answer 23

subtract first equation from second equation and find x and then corresponding y.