Answer:
To solve the system of linear equations:
x_1 + 3x_2 = 1 ...(1)
2x_1 + 5x_2 = 3 ...(2)
We can use the method of elimination to eliminate one of the variables. To do this, we multiply equation (1) by 2, and subtract it from equation (2), as follows:
2(x_1 + 3x_2 = 1) => 2x_1 + 6x_2 = 2 ...(3)
2x_1 + 5x_2 = 3 ...(2)
(2x_1 + 6x_2 = 2) ...(3)
-x_2 = 1
Thus, we have found that x_2 = -1.
We can substitute this value of x_2 into either equation (1) or (2) to solve for x_1. Let's use equation (1):
x_1 + 3(-1) = 1
x_1 - 3 = 1
x_1 = 4
Therefore, the solution to the system of linear equations is x_1 = 4, x_2 = -1.
So the solution set is {(4, -1)}.