Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x - 5y = 24 2x + 3y = -10 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.)

it has one and only one solution.

Step-by-step explanation:

The given system of equations is expressed as

4x - 5y = 24 - - - - - - - - - - - - -1

2x + 3y = -10 - - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 1 and equation 2 by 2. It becomes

4x - 5y = 24

4x + 6y = - 20

Subtracting, it becomes

- 11y = 44

Dividing the left hand side and the right hand side of the equation by

- 11, it becomes

- 11y/- 11 = 44/- 11

y = - 4

Substituting y = - 4 into equation 2, it becomes

2x + 3 × - 4 = -10

2x - 12 = - 10

2x = - 10 + 12

2x = 2

Dividing the left hand side and the right hand side of the equation by

2, it becomes

2x/2 = 2/2

x = 1