Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5/4x-2/3y=8 and 1/4x+5/3y=7

Answer 1

has only one solution:
`x=8, y=3`

Explanation:

`\left \{ {{(5x)/(4) -(2y)/(3)=8(equation 1)} \atop {(x)/(4) +(5y)/(3) =7(equation 2)}} \right\\`

substract
`(1)/(5)`×(equation 1) from equation2

`\left \{ {{(5x)/(4) -(2y)/(3)=8(equation 1)} \atop {0x +(9y)/(5) =(27)/(5)(equation 2)}} \right\\`

from equation 2 we obtain

`y=(27)/(9) =3`

and we replace 3 in equation 1

`(5x)/(4) -(2(3))/(3) =8\\\\(5x)/(4) =10\\\\x=(40)/(5) =8`