8x - 3y = 5xy; 6x - 5y = - 2xy
Answers
Answer:
elimination method we solve a system of two linear equations of two variables by eliminating one variable after operating the equations,
Given equations,
8x-3y=5xy,
\implies \frac{8}{y}-\frac{3}{x}=5----(1)⟹
y
8
−
x
3
=5−−−−(1)
6x-5y=-2xy
\implies \frac{6}{y}-\frac{5}{x}=-2----(2)⟹
y
6
−
x
5
=−2−−−−(2)
∵ LCM(8, 6) = 24,
3 × equation (1) - 4 × equation (2),
We get,
-\frac{9}{x}+\frac{20}{x}=15 + 8−
x
9
+
x
20
=15+8
\frac{-9+20}{x}=23
x
−9+20
=23
\frac{11}{x}=23
x
11
=23
\implies x = \frac{11}{23}⟹x=
23
11
From equation (1),
\frac{8}{y}-\frac{69}{11}=5
y
8
−
11
69
=5
\frac{8}{y}=5+\frac{69}{11}
y
8
=5+
11
69
\frac{8}{y}=\frac{55+69}{11}
y
8
=
11
55+69
\frac{8}{y}=\frac{124}{11}
y
8
=
11
124
\implies y = \frac{88}{124}=\frac{22}{31}⟹y=
124
88
=
31
22