the system of equations 3x -6y=20 and 2x-4y=3 Is
dependent
consistent
inconsistent
independent
I think its inconsistent because somehow i ended up with 12=49.. can u show me the work too.I think i did it wrong.
If you multiply the first equation by 2 and the second equation by 3 you get the following set of equations:
6x-12y=40
6x-12y=9
They can not both be true. They are inconsistent with each other.
To determine whether the system of equations is dependent or independent, we need to solve the equations and see if we end up with a consistent or inconsistent system.
Let's solve the system of equations step by step:
Equation 1: 3x - 6y = 20 [Multiply equation 1 by 2 to simplify]
Equation 2: 2x - 4y = 3
Step 1: Multiply equation 1 by 2:
6x - 12y = 40
Step 2: Rearrange equation 2:
2x = 4y + 3
Step 3: Substitute equation 2 into the modified equation 1:
6x - 12y = 40
6x - 12(4y + 3) = 40
6x - 48y - 36 = 40
6x - 48y = 76
Step 4: Combine like terms:
6x - 48y = 76
Now, compare this equation (6x - 48y = 76) with the original equation 2 (2x - 4y = 3).
From the comparison, we can see that the two equations are not equivalent. If the two equations have different slopes (the coefficients of x differ), then the system is inconsistent, meaning there is no solution that satisfies both equations.
Therefore, your conclusion that the system of equations is inconsistent is correct.
To determine whether the system of equations is dependent, consistent, inconsistent, or independent, we will solve the equations and analyze the results.
1) Start with the given system of equations:
3x - 6y = 20 -- (Equation 1)
2x - 4y = 3 -- (Equation 2)
2) We can solve this system of equations by using the method of substitution or elimination. Let's use the method of substitution for this example:
From Equation 2, we can solve it for x:
2x = 4y + 3 -> x = (4y + 3)/2
3) Substitute the expression for x into Equation 1:
3((4y + 3)/2) - 6y = 20
Simplify this equation:
(12y + 9)/2 - 6y = 20
12y + 9 - 12y = 40
9 = 40
4) Looking at the resulting equation, we can see that 9 does not equal 40. Therefore, the system of equations is inconsistent, indicating that there is no solution that satisfies both equations simultaneously.
Hence, your initial intuition was correct, and the system of equations 3x - 6y = 20 and 2x - 4y = 3 is inconsistent.