Question

2) Solve the following simultaneous equations.
(x+10)(y-2)= xy; (x-15) (y+6)=xy.​

Answer 1

Step-by-step explanation:

(xy-2x+10y-20)=(xy+6x-15y-90)

(xy-xy)-(2x+6x)+(10y+15y)-(20-90)

(0)-(8x)+(25y)-(-70)

8x+25y+70 __________.1.

let

x=1

8×1+25y+70

25y+78=0

y=78/25

y=3.12

____.1.

8x+25×3.12+70=0

8x+78+70=0

8x+148=0

8x=-148

x=-148/8

x=18.5 ans

Answer 2

The solution of given equations is (55,13).

Step-by-step explanation:

$(x+10)(y-2)=xy$

$xy-2x+10y-20=xy$

$-2x+10y=xy-xy+20=20$

$-2x+10y=20$....(1)

$(x-15)(y+6)=xy$

$xy+6x-15y-90=xy$

$6x-15y=90-xy+xy=90$

$2x-5y=45$....(2)

Adding equation (1) and (2)

$5y=65$

$y=\frac{65}{5}=13$

Substitute the value in equation (1)

$-2x+10\times 13=20$

$-2x+130=20$

$-2x=20-130=-110$

$x=\frac{110}{2}=55$

Hence, the solution of given equations is (55,13).

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