Question 106284


Let x=the larger integer
And let y=the smaller integer

Now we are told that x-y=9--------------------------eq1

We are also told that 5y=3x+7-----------------------eq2

From eq1, substitute x=y+9 into eq2 and we get:

5y=3(y+9)+7  get rid of parens

5y=3y+27+7  subtract 3y from both sides
5y-3y=3y-3y+27+7  collect like terms
2y=34  divide both sides by 2

y=17------------------the smaller integer
From eq1, x=9+y=9+17=26 --------the larger integer

CK

x-y=9
26-17=9
9=9
also
5y=3x+7
5*17=3*26+7

85=78+7
85=85


Another way to solve this problem:

Let x=the larger integer
Then x-9= the smaller integer 

Now we are told that:

5(x-9)=3x+7  get rid of parens

5x-45=3x+7  subtract 3x from and add 45 to both sides

5x-3x-45+45=3x-3x+45+7  collect like terms

2x=52  divide both sides by 2

x=26----------------the larger integer

x-9=26-9=17---------------the smaller integer


Hope this helps----ptaylor