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

Answer:

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

Step-by-step explanation:

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

substract  $\frac{1}{5}$×(equation 1) from equation2

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

from equation 2 we obtain

$y=\frac{27}{9} =3$

and we replace 3 in equation 1

$\frac{5x}{4} -\frac{2(3)}{3} =8\\\\\frac{5x}{4} =10\\\\x=\frac{40}{5} =8$