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Question
Find the values of x and y if
`[[X + 10,Y^2 + 2Y],[0, -4]]`=`[[3x +4,3],[0,y^2-5y]]`
Solution
Here,
x+10=3x+4 [∵ All the corresponding elements of the matrix are equal]
⇒x−3x=4−10
⇒−2x=−6
∴ x=3
Also,
y2+2y=3
⇒y2+2y−3=0
⇒y2+3y−y−3=0
⇒y(y+3)−1(y+3)=0
⇒(y+3)(y−1)=0
⇒y+3=0 or y−1=0
⇒y=−3 or y=1
Now,
−4=y2−5y
⇒y2−5y+4=0
⇒y2−4y−y+4=0
⇒y(y−4)−1(y−4)=0
⇒(y−4)(y−1)=0
⇒y−4=0 or y−1=0
⇒y=4 or y=1
Since `y^2+2y=3 `and `y^2-5y=-4` must hold good simultaneously, we take the common solution of these two equations.
Thus,
y = 1, x = 3 and y = 1
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