# Question #41282

##### 3 Answers

11 and 16

#### Explanation:

First, write the problem in the form of a system of equations:

Next, using substitution, combine the two equations replacing x in the first equation with the value of x in the second:

Then, simplify and solve for y:

Finally, plug in the value of y into the original equation and solve for x:

You can check your values of x and y by plugging them into both original equations and determining if they fulfill it:

#### Explanation:

#"let the 2 numbers be "x" and "y#

#"then "x+y=27color(white)(x);x>y#

#"larger number "x=2y-6#

#rArr2y-6+y=27#

#rArr3y-6=27#

#"add 6 to both sides"#

#rArr3y=33rArry=11#

#"substitute into "x+y=27#

#rArrx+11=27rArrx=16#

#### Explanation:

To solve it, assumed the following variables:

Let x= the smaller number

Let y= the bigger number

Now, formulate equations that relate the assumed numbers as prescribed in the problem; hence,

Then, solve the problem through substitution method; given the value of

Check: