Question

Matt is 9 years older than twice Emily’s age. The sum of their ages is 90. Write a system of linear equations to solve find Matt and Emily’s ages. What is Matt’s age?Separate you equations and final answer by commas.

Answer 1

Let, Matt's age be x years and Emily's age be y years.

Matt is 9 years older than twice Emily’s age .

It can be written as,

`x=2y+9\ldots\ldots\ldots\ldots(1)`

And sum of their ages is 90

`x+y=90\ldots\ldots\ldots\ldots\text{.}(2)`

Put the value of x from equation (1) in equation (2).

`\begin{gathered} x+y=90 \\ (2y+9)+y=90 \\ 3y=81 \\ y=27 \end{gathered}`

Put the value of y in equation (1),

`\begin{gathered} x=2y+9 \\ x=2(27)+9 \\ x=63 \end{gathered}`

Hence, the Matt's age is x= 63 years and Emily's age is y=27 years.