[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let the two digit number be ' xy '
where, x is the ten's place digit, and y is one's place digit, now let's proceed further ~
The origin number can be written as :
[tex]\qquad \sf \dashrightarrow \: 10x + y[/tex]
[ because x is at ten's place ]
of the digits are swapped, the new number will be :
[tex]\qquad \sf \dashrightarrow \: 10y + x[/tex]
According to conditions provided in the question : -
[tex]\qquad \sf \dashrightarrow \: 10x + y = 7 \times (x + y)[/tex]
[tex]\qquad \sf \dashrightarrow \: 10x + y = 7x + 7y[/tex]
[tex]\qquad \sf \dashrightarrow \: 10x - 7x + y - 7y= 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x - 6y = 0 \: \: \: \: \: \: [/tex]
[tex]\qquad \sf \dashrightarrow \: x - 2y = 0 \: \: \: \: \: \: - (1)[/tex]
here we got our first equation, let's find the other one ~
[tex]\qquad \sf \dashrightarrow \: (10x + y) - 18= 10y + x[/tex]
[tex]\qquad \sf \dashrightarrow \: 10x - x + y - 10y = 18[/tex]
[tex]\qquad \sf \dashrightarrow \: 9x - 9y = 18[/tex]
[tex]\qquad \sf \dashrightarrow \: x - y = 2 \: \: \: \: \: \: - (2)[/tex]
we got our second equation ~
Now it's time to subtract equation (1) from equation (2) :
[tex]\qquad \sf \dashrightarrow \:( x - y ) - (x - 2y)= 2 - 0[/tex]
[tex]\qquad \sf \dashrightarrow \: \cancel{x }- y - \cancel{x} + 2y= 2 - 0[/tex]
[tex]\qquad \sf \dashrightarrow \: y= 2 [/tex]
hence, value of y is 2, use this value in equation (2) to find x ~
[tex]\qquad \sf \dashrightarrow \: x - y= 2 [/tex]
[tex]\qquad \sf \dashrightarrow \: x - 2= 2 [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 4 [/tex]
Therefore, the required number is xy = 42
