Find the values of x and y if

$open square brackets table row cell straight x plus 10 end cell cell straight y squared plus 2 straight y end cell row 0 cell negative 4 end cell end table close square brackets equals open square brackets table row cell 3 x plus 4 end cell 3 row 0 cell y squared minus 5 y end cell end table close square brackets$

Solution

We are given that
$open square brackets table row cell straight x plus 10 end cell cell straight y squared plus 2 straight y end cell row 0 cell negative 4 end cell end table close square brackets equals open square brackets table row cell 3 straight x plus 4 end cell 3 row 0 cell straight y squared minus 5 straight y end cell end table close square brackets$

From the definition of equality of matrices, we have,
x + 10 = 3x + 4, y²+2y=3, -4= y²–5y
Now x + 10 = 3 x + 4 ⇒2x= 6 ⇒ ,x = 3
y² + 2 y – =3 ;⇒ y²+2y – 3 =0 ⇒ (y + 3) ( y –1) = 0 ⇒ y = 1. –3
– 4 = y ² – 5 y ⇒ y² – 5 y + 4 = 0 ⇒ ( y – 1) ( y – 4) = 0 ;⇒ y – 1. 4
Since both the equations y² + 2 y =3 and - 4 ='y² -5 y are to be satisfied, so we have y'= 1
∴ x = 3. y = I.

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