# What are x and y given that x + 2y = 5 and 2x +4y = 6?

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We have the two equations:

x + 2y = 5 … (1)

2x + 4y = 6 … (2)

From (1) we have

x + 2y = 5

=> 2x + 4y = 10

And from (2) we have 2x + 4y = 6.

Both of these cannot be true as it would imply 6 = 10.

Looking at (1) and (2) it can be seen that we cannot derive the value of x and y from them.

**Therefore the system of equations cannot yield a valid solution.**

Given the system of equations:

x+2y = 5........(1).

2x+4y = 6......(2).

To solve for the solution for (x,y).

We see that two lines a1x+b1y=c1 and a2x+b2y= c2 = 0 are parallel or have the same slope if a1/a2 = b1/b2 but not equal to c1/c2.

a1 = 1, b1 = 2, and c1 = 5. a2 = 2, b2 = 4 and c2 = 6. So a1/a2 = b1/b2 = 1/2. But c1/c2 = 5/6.

Therefore the given lines x + 2y = 5 and 2x +4y = 6 are parallel. So **the lines do not intersect.**

Therefore **there is no solution** which satisfy both system of equations.equations.

We'll change the 1st equation in x = 5 - 2y

We'll substitute it into the second equation:

2(5 - 2y) +4y = 6

We'll remove the brackets:

10 - 4y + 4y = 6

We'll eliminate like terms and we'll get:

10 = 6 impossible!

**So, the system formed form the given equations has no solutions!**