The larger number is five more than the smaller number. Four more than three times the smaller number is twice the larger number. Find both numbers.

Larger number = 11

Smaller number = 6

Step-by-step explanation:

Let the larger number = x

Let the smaller number = y

x - y = 5

3y + 4 = 2x       Subtract 2x

-2x + 3y + 4 = 0

Multiply  the first equation by 2. Write the second equation underneath

2x - 2y = 10

-2x + 3y + 4 = 0

add

y + 4 = 10  

Subtract from both sides

y = 10 - 4

y = 6

x - y = 5

x - 6 = 5                Add 6 to both sides

x = 5 + 6

x = 11

Step-by-step explanation:

x       ← the smaller number

x+5    ←  five more than the smaller number - the larger number

3x    ← three times the  smaller number

3x+4   ← four more than three times the  smaller number

2(x+5)   ← twice the larger number

3x + 4 = 2(x + 5)

3x + 4 = 2x + 10

   -4         -4

     3x = 2x + 6

  -2x       -2x

      x  =  6

x+5 = 6 + 5 = 11

Check:   3•6 + 4 = 22;  22:2 = 11

a. is correct

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )