how do you solve this problem by elimination method
3x+4y=2
6x+8y=4
They are the same equation, and do not have a unique solution. The second equation is the first multiplied by 2.
To solve this system of equations using the elimination method, the goal is to eliminate one variable by adding or subtracting the equations. Here's how you can solve it step by step:
1. Start by multiplying the first equation by 2 (to make the coefficients of x in both equations equal):
2 * (3x + 4y) = 2 * 2
This simplifies to:
6x + 8y = 4
2. Now you have the second equation as 6x + 8y = 4.
Line up the two equations vertically:
6x + 8y = 4
6x + 8y = 4
3. Subtract the second equation from the first equation (or vice versa) to eliminate the x variable. In this case, subtract the first equation from the second equation:
(6x + 8y) - (6x + 8y) = 4 - 4
This simplifies to:
0 = 0
4. Since 0 = 0, this means that the two equations are equivalent or dependent. This tells us that the system of equations has infinitely many solutions, and the equations represent the same line.
Therefore, the solution to the system of equations is all values of x and y that satisfy the equation 6x + 8y = 4.