Question

Matt is 9 years older than twice Emily's age. The sum of their ages is 90, write the system of linear equation to find Matt and Emily's ages. What is Matt's age?

Answer 1

Matt 63, Emily 27

Explanation:

You have two incognita here: Matt's age and Emily's age.

You also know that Matt is nine years older than twice Emily's age, and they both ages sum 90.

If Matt is
`X` and Emily is
`Y`, you can say
`X+Y=90` years and
`X=2Y+9` years.

Now you have two equations and two incognitas, you can solve it.

First, clear the x and equal both equation

`X=2Y+9`

`X+Y=90`

`X=90-Y`

Then, solve and found the value of Y and now, can resolve the X

`90-Y=2Y+9`

`90-9=2Y+Y`

`81=3Y`

`81/3=Y`

`27=Y`

Go back to X equation

`X=2Y+9`

`X=2*27+9`

`X=63`

Answer 2

x+y = 90

x=2y+9

2y+9+y=90

3y=81

y= 27 Emily's age

x= 2*27+9 = 63 Matt's age