For the system of equations that follows, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is consistent. If the system is consistent and involves no free variables, use back substitution to find the unique solution. If the system is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. x₁ + 3x₂ + x₃ + x₄ = 3;
2x₁ - 2x₂ + x₃ + 2x₄ = 8;
x₁ - 5x₂ + x₄ = 5

Step-by-step explanation:

From the question we are told that

System of equations given as

x₁ + 3x₂ + x₃ + x₄ = 3;

2x₁ - 2x₂ + x₃ + 2x₄ = 8;

x₁ - 5x₂ + x₄ = 5

Matrix form

Generally the echelon reduction is mathematically applied as

Add -2 times the 1st row to the 2nd row

Multiply the 2nd row by -1/8  

Add -1 times the 2nd row to the 3rd row

Multiply the 3rd row by -8/41

Add -1/8 times the 3rd row to the 2nd row

Add -1 times the 3rd row to the 1st row

Add -3 times the 2nd row to the 1st row

The population of the town will be 86,000 in 2015.

Explanation: Between 1950 and 2010 (60 years) , the population rose by 36,000. To find out how much the pop. rose each year, we divide 36,000 by 60 (the amount of years) and get 600. Between 2010 and 2015 there are 5 years. 5x600 = 3,000. 3,000 + 83,000 (population in 2010) is 86,000.