Solve by elimination method
2x + 3y =1
4x + 6y =2
What is the solution of the system
N there is no solution
To solve the system of equations using the elimination method, we can multiply the first equation by 2 to make the coefficients of x in both equations equal:
2(2x + 3y) = 2(1)
4x + 6y = 2
Now, we can see that the second equation is actually equivalent to the first equation, meaning that the system of equations is dependent, and there are infinitely many solutions. In other words, the two equations represent the same line.
To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can multiply the first equation by 2 to make the coefficients of x in both equations equal.
The original equations are:
1) 2x + 3y = 1
2) 4x + 6y = 2
Multiplying equation (1) by 2 gives:
3) 4x + 6y = 2
Now we can see that equations (2) and (3) are the same. This means that these equations represent the same line, and therefore, they are dependent equations. So, there are infinitely many solutions to this system of equations.
Geometrically, the two equations represent the same line, which means they are parallel. Hence, they will never intersect and there is no unique solution for this system.
Therefore, the solution to the system of equations is that there is no solution (N).