solve by the elimination method
3x+4y=3
6x+8y=6
help please
To solve the system of equations using the elimination method, we want to eliminate one variable (either x or y) by multiplying one or both of the equations by certain numbers so that when you add or subtract the two equations, one of the variables will be eliminated.
Let's start solving the system of equations using the elimination method:
Step 1: Multiply the first equation by -2.
-2(3x + 4y) = -2(3)
This gives us:
-6x - 8y = -6
Step 2: Rewrite the second equation.
6x + 8y = 6
Step 3: Add the two equations together.
(-6x - 8y) + (6x + 8y) = -6 + 6
The -6x and 6x terms will cancel out, and the -8y and 8y terms will also cancel out. This leaves us with:
0 = 0
Step 4: Analyze the result.
In this case, we end up with the equation 0 = 0, which means that the two original equations are actually equivalent. This indicates that the two equations represent the same line, and therefore, they have infinitely many solutions.
So, the system of equations is consistent and dependent, meaning any values of x and y that satisfy one equation will satisfy the other equation as well. Therefore, we can say that there are an infinite number of solutions to this system of equations.
To solve the given system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations.
Step 1: Multiply the first equation by 2 to make the coefficient of x in both equations the same:
2(3x + 4y) = 2(3)
This simplifies to:
6x + 8y = 6
Now we have:
6x + 8y = 6
6x + 8y = 6
Step 2: Subtract the first equation from the second equation:
(6x + 8y) - (6x + 8y) = 6 - 6
This simplifies to:
0 = 0
The equation 0 = 0 is a true statement, indicating that the two equations are dependent and consistent. Both equations represent the same line or infinitely many solutions.
Therefore, there are infinitely many solutions to the given system of equations.