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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?

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musiclover10045

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



vicobusso

Answer:

Matt 63, Emily 27

Step-by-step 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 [tex]X[/tex] and Emily is [tex]Y[/tex], you can say  [tex]X+Y=90[/tex] years and [tex]X=2Y+9[/tex] years.

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

First, clear the x and equal both equation

[tex]X=2Y+9[/tex]

[tex]X+Y=90[/tex]

[tex]X=90-Y[/tex]

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

[tex]90-Y=2Y+9[/tex]

[tex]90-9=2Y+Y[/tex]

[tex]81=3Y[/tex]

[tex]81/3=Y[/tex]

[tex]27=Y[/tex]

Go back to X equation

[tex]X=2Y+9[/tex]

[tex]X=2*27+9[/tex]

[tex]X=63[/tex]

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