Question

$2x + 3y = 55 \\ 5y + xy = 125$
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Answer 1

Step-by-step explanation:

$2x+3y=55$                          ₋₋₋₋1

$5y+xy=125$

$y(5+x)=125$

$y=\frac{125}{5+x}$                                  ----2

putting value of y in equation 1, we get

$2x+3*\frac{125}{5+x}=55\\\\ 10x+2x^{2} +275=275+55x\\\\2x^{2} -45x+100=0\\\\2x^{2} -40x-5x+100=0\\\\2x(x-20)-5(x-20)=0\\\\(2x-5)(x-20)=0\\\\x=\frac{5}{2}, x=20$

now put the values of x in 1

when $x=\frac{5}{2}$, we get $y=\frac{50}{3}$

when $x=20$, we get $y=5$

hope this helps