The solution to the system of equations is (x1 ,x2 ,x3 ,x4 )=(−282,−1,0,0).
The equation you sent me is a system of four linear equations with four unknowns.
To solve it, you can use Gaussian elimination.
This method involves eliminating the variables one at a time until you are left with a single equation in a single variable.
Here are the steps to solve the system of equations using Gaussian elimination:
Write the system of equations in augmented matrix form.
[5 -2 3 1 2013]
[2 3 1 1 -3]
[0 0 -1 2 -3]
[0 0 0 4 4]
Eliminate x 1 from the second, third, and fourth equations.
[5 -2 3 1 2013]
[0 7 4 -1 -1979]
[0 0 -1 2 -3]
[0 0 0 4 4]
Eliminate x2 from the third and fourth equations.
[5 -2 3 1 2013]
[0 7 4 -1 -1979]
[0 0 -1 2 -3]
[0 0 0 4 0]
Solve the fourth equation for x3 .
x_3 = \frac{0}{4} = 0
Substitute 0 for x3 in the third equation and solve for x2.
-x_2 = 2 - 3
x_2 = -1
Substitute -1 for x2 in the second equation and solve for x1 .
7x_1 - 4 - 1 = -1979
7x_1 = -1974
x_1 = -282
Therefore, the solution to the system of equations is (x1 ,x2,x3 ,x4 )=(−282,−1,0,0).