How can you solve this by using system of equations by elimination using multiplication??

Question

The sum of the digits of a 2 digit number is 7. If the digits are reversed, the new number is 3 less than 4 times the original number. Find the number.

Answer 1

Make some equations, and then sort it out from there:

let's call x the first number and y the second number.
1) original number = x*10 + y
2) x + y = 7
3) reversed number = y*10 + x
4) reversed number = 4*original - 3

plugging 1) into 4) we get:
= 4*(x*10 + y) - 3
= 40x + 4y - 3

since 3) = 4) we can write:
10y + x = 40x + 4y - 3
6y = 39x - 3 (divide out the 3...)
2y = 13x - 1
y = (13x - 1)/2

we know from 2) that x+y = 7, OR y = 7-x.
We can substitute that in for y in the equation above:
7-x = (13x -1)/2
14 - 2x = 13x - 1
15x = 15
x = 1

again from 2) we know that x + y = 7, so now we can just plug in the value of x we found:

1 + y = 7
y = 6

So, the original number given by equation 1) is:
= 10*x + y
= 10*1 + 6
= 16

Answer 2

truly you opt for the resultant equations to have between the variables opposites of one yet another so even as they're extra, you get 0 and are left with merely one variable. there are countless selections in a great number of cases to attempt this. Your celebration, I word the 2y and understand the different of it truly is -2y. contained in the 2d equation there's a -y. If i multiply that via 2, i receives -2y. So my new 2d equation will change into 2x - 2y = -26 including the first one to it 3x + 2y=-9, i'm getting 5x + 0y = -35 divide each and each part via 5 and get x = -7 wish that permits some. although, i'd have expanded the 2d equation via -3, getting a -3x which, even as extra to the first would cancel out the x words.

Answer 3

Let the original number be: 10a + b
Say 23. Let a = 2; b = 3. Then 23 = 10a + b

Now: a + b =7 --------(1)
10b + a = 4(10a + b) - 3 ------(2)

Simplify (2). Solve system of equations

Answer 4

Consider:-
(1,6) (2,5) (3,4) (4,3) (5,2)
and test each one:-

Let original number be 16
1 + 6 = 7
61 = 4 x 16 - 3 = 61

Thus the first test has produced the answer and there is no need to carry out more tests.

Answer is 16

Answer 5

let the digit in ten's place be x and that in unit's place be y
Therefore,the number is 10x+y
According to the problem,
x+y=7.......(1)
10y+x=4(10x+y)-3
=> 10y+x=40x+4y-3
=>x-40x+10y-4y= -3
=>-39x+6y= -3........(2)
Multiplying eqn 1 by 39 and eqn 2 by 1,we get,
39x+39y=273
-39x+6y= -3
(adding) 45y=270
=>y=6
Putting the value of y in eqn 1,we get
x=1
kTherefore,the number is 16