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