Answer: The value of x=3 and the value of y=1.
Step-by-step explanation: The given equations are [tex]21x + 47y = 110[/tex] and [tex]47x + 21y = 162[/tex]
To find: The values of [tex]x[/tex] and [tex]y[/tex]
Solution: Given equation
[tex]21x + 47y = 110[/tex] ... (1)
[tex]47x + 21y = 162[/tex] ... (2)
Now we will find the values of [tex]x[/tex] and [tex]y[/tex] using Substitution method.
Considering the equation (1)
[tex]21x + 47y = 110[/tex]
Subtracting [tex]47y[/tex] on the left hand side and right hand side as well
[tex]21x + 47y - 47y = 110 - 47y[/tex]
[tex]21x = 110- 47y[/tex]
Now, dividing by 21 on both the sides, we will get
[tex]\frac{21x}{21} =\frac{ 110- 47y}{21}[/tex]
[tex]x=\frac{ 110- 47y}{21}[/tex] ...(A)
Now, putting the value of [tex]x[/tex] in equation (2), we get
[tex]47(\frac{ 110- 47y}{21}) + 21y = 162[/tex]
[tex](\frac{5170-2209y}{21}) + 21y = 162[/tex]
Now, taking LCM on the LHS of the equation
LCM of 21 and 1 is 21
[tex]\frac{5170-2209y+441y}{21} = 162[/tex]
Multiplying 21 on both the sides we get,
[tex]5170-2209y+441y = 3402[/tex]
[tex]1768y= 1768[/tex]
[tex]y= \frac{1768}{1768}[/tex]
[tex]y= 1[/tex]
Now, putting the values of y in equation (A)
[tex]x=\frac{ 110- 47(1)}{21}[/tex]
[tex]x=\frac{63}{21}[/tex]
[tex]x=3[/tex]
Therefore, the value of x=3 and the value of y=1.