Question

etermine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 3 2 x − 2y = 4 x + 1 3 y = 2 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =

Answer 1

(32/15, -2/5)

Explanation:

(1) ³/₂x - 2y = 4

(2) x + ⅓y = 2

(3) 3x - 4y = 8 Multiplied (1) by 2

(4) 3x + y = 6 Multiplied (2) by 3

5y = -2 Subtracted (3) from (4)

(5) y = -⅖ Divided each side by 5

x + ⅓(-⅖) = 2 Substituted (5) into (2)

x - ²/₁₅ = 2

x = 2 + ²/₁₅ Added ²/₁₅ to each side

x = 32/15

The system of equations has only one solution: (32/15, -2/5).