Question

Question #41282

Answer 1

11 and 16

Explanation:

First, write the problem in the form of a system of equations:
`27 = x + y`
`x = 2y - 6`

Next, using substitution, combine the two equations replacing x in the first equation with the value of x in the second:
`27 = (2y - 6) +y`

Then, simplify and solve for y:
`27 = 3y - 6`
`33 = 3y`
`y = 11`

Finally, plug in the value of y into the original equation and solve for x:
`27 = x + 11`
`x = 16`

You can check your values of x and y by plugging them into both original equations and determining if they fulfill it:
`27 = 11 + 16`
`27 = 27` Check

`16 = 2(11) - 6`
`16 = 22 - 6`
`16 = 16` Check

Answer 2

`11" and "16`

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`

Answer 3

`"The numbers are " 11 and 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,

`x+y=27->eq.1`
`y=2x-6->eq.2`

Then, solve the problem through substitution method; given the value of `y` as shown in the formulated `eq.2` above. So that:

`x+color(red)(y)=27`, substitute the value of y

`x+color(red)((2x-6))=27`, simplify the equation

`x+color(red)(2x-6)=27`, combine like terms

`3x-6=27`, add `6` both sides of the equation to isolate the term with variable `x`.

`3x-6+6=27+6`, simplify and combine like terms

`3x=33`, divide both sides by `3`

`x=11`

`"Therefore:"`

`color(red)(x=11)`

`y=2x-6->eq.2`, substitute the value of `x=11`

`y=2(11)-6`

`y=22-6`

`color(blue)y=16`

Check:
`color(red)(x)+color(blue)y=27`
`11+16=27`
`27=27`