Question

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. X₁ + 4x₂ = 9 , 2x₁ + 7x₂ = 14

Answer 1

To solve the system of equations, we use elementary row operations to eliminate variables and find the values of x₁ and x₂. The solution to the system is x₁ = 7/3 and x₂ = 5/3.

Step-by-step explanation:

Solving the System of Equations using Elementary Row Operations:

1. Write the equations in matrix form:
2. | 1 4 | | 9 |
3. | 2 7 | | 14 |
4. Apply row operations to eliminate the 2 in the bottom left corner:
5. | 1 4 | | 9 |
6. | -1 -1 | | -4 |
7. Apply row operations to eliminate the -1 in the bottom left corner:
8. | 1 4 | | 9 |
9. | 0 3 | | 5 |
10. Solve the equation 3x₂ = 5:
11. x₂ = 5/3
12. Substitute the value of x₂ into the first equation to solve for x₁:
13. x₁ + 4(5/3) = 9
14. x₁ + 20/3 = 27/3
15. x₁ = 7/3
16. Therefore, the solution to the system of equations is x₁ = 7/3 and x₂ = 5/3.