I find from the first equation that x = 3y and plugging in to the second equation we get

o.2y+37(-3y)=23
0.2y-111y=23
-110.8y=23
y=-23/110.8
x=69/110.8
need help to understand why the elimination process in not work in this linear equation?

without both equations, I do not have a clue either.

12y +4x=0

0.2y+37x=23
does this help

The elimination method is a common method used to solve a system of linear equations by eliminating one variable through addition or subtraction of the equations. In this case, it seems like the elimination process did not work because the substitution step was performed incorrectly.

Let's go through the steps to see what went wrong:

1. Start with the system of equations:
Equation 1: x = 3y
Equation 2: 0.2y + 37(-3y) = 23

2. Substitute the value of x from Equation 1 into Equation 2:
0.2y + 37(-3y) = 23
0.2y - 111y = 23

At this point, everything is correct.

3. Combine like terms:
-110.8y = 23

Up to this step, everything is still fine. However, the next calculation is where the mistake occurred.

4. Solve for y by dividing both sides of the equation by -110.8:
y = -23/110.8

It seems that you made an error in the division. The correct calculation should result in y = -0.2077 (rounded to four decimal places).

5. Now that we have the value of y, you can substitute it back into Equation 1 to find x:
x = 3y = 3(-0.2077) = -0.6231 (rounded to four decimal places)

So the correct solution is x = -0.6231 and y = -0.2077.

In summary, the elimination process itself was not the issue, but rather there was a mistake made during the substitution and calculation step. Double-checking the calculations can help avoid errors and ensure an accurate solution.