using echelon method
4x-2y=9
20x-10y=27
pls help with problem. Once I get 24x -2y 36 I'm confused after that.
Somebody expects you to solve a 2 by 2 system using matrices with echelon reduced form ??
That's like going to the corner store to buy milk in an 18 wheeler tractor-trailer.
Furthermore the system has no solutions, since if you multiply the first by 5, you get
20x - 10y = 45
now subtract the two to get
0 = 18
CONTRADICTION, so no solution.
Thanks Reiny
To solve the system of equations using the echelon method, you need to follow a series of steps. Let me guide you through the process.
1. Write the system of equations in matrix form:
| 4 -2 | | x | = | 9 |
| 20 -10 | | y | | 27 |
2. The first step is to eliminate the variable x from the second row. Multiply the first row by -5 and add it to the second row:
| 4 -2 | | x | = | 9 |
| 0 0 | | y | | -18 |
3. Simplify the second row to get a new matrix:
| 4 -2 | | x | = | 9 |
| 0 0 | | y | | -18 |
4. Solve for y. Since the second row contains only zeros, we see that y can take any value. So we set y = t, where t is a parameter.
5. Substitute the value of y into the first equation and solve for x:
4x - 2t = 9
x = (9 + 2t) / 4
6. The solution to the system of equations is given by:
x = (9 + 2t) / 4, y = t
Now, let's move on to the next step:
7. To continue using the echelon method, we need to eliminate the value of x in the second equation. Multiply the first row by -5 and add it to the second row:
| 4 -2 | | x | = | 9 |
| 0 0 | | y | | -18 |
8. Simplify the second row to get a new matrix:
| 4 -2 | | x | = | 9 |
| 0 0 | | y | | 0 |
9. At this point, we have a row of zeros, which means there are infinitely many solutions to the system of equations. The value of x doesn't affect the second equation (0y = 0), so any value of x will work.
10. Therefore, the solution to the system of equations is:
x = (9 + 2t) / 4, y = t; where t is a parameter and x can take any real value.
I hope this step-by-step explanation helps you understand how to solve the system of equations using the echelon method. Let me know if you have any further questions!