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Question

Solve the following simultaneous equation:
$$4x+5y = 10; \, \, 5x+4y=17$$


A
x=3y=2
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B
x=1y=4
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C
x=0y=3
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D
x=5y=2
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Solution

The correct option is D $$x=5\, \, y=-2$$
$$4x+5y=10$$              .....(1)
$$5x+4y=17$$              .......(2)

Adding (1) and (2). we get
$$9x+9y=27$$
$$\Rightarrow x+y=3$$               ......(3)

Now, subtracting (1) from (2). we get,
$$x-y=7$$                                   .......(4)

Adding (3) and (4). we get
$$2x=10$$
$$\Rightarrow x=5$$            

Now, subtracting (3) from (4). we get,
$$-2y=4$$   
$$\Rightarrow y=-2$$           

$$\therefore x=5 , y=-2$$ 
Option D is correct.                         

Mathematics

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