charleen14
contestada

Reese pick two numbers, X and Y. she told her friend that the sum of the two numbers is 9 and the difference of the two numbers is 17.
a.Write two different linear equations that model what Reese told her friend.



b.Solve the system of linear equations using the substitution method. What two numbers did Reese pick?

Respuesta :

a.
x + y = 9
x - y = 17

b.
[tex]x = 9 - y[/tex]
Substitute that into
[tex]9 - y - y = 17 \\ 9 - 2y = 17 \\ 2y = - 8 \\ y = - 4[/tex]

Substitute that into
[tex]x = 9 - ( - 4) \\ x = 13[/tex]

x = 13, y = - 4

Hope this helps. - M
boffeemadrid

The equations and two numbers are required.

The equations are [tex]x+y=9[/tex] and [tex]y-x=17[/tex]

The value of X is -4 and Y is 13.

The two numbers are X and Y

The sum is 9 and difference is 17

[tex]x+y=9\\\Rightarrow y=9-x[/tex]

[tex]y-x=17[/tex]

Substituting y value in second equation

[tex]9-x-x=17\\\Rightarrow 9-2x=17\\\Rightarrow x=\dfrac{17-9}{-2}\\\Rightarrow x=-4[/tex]

[tex]y=9-x=9-(-4)\\\Rightarrow y=13[/tex]

The value of X is -4 and Y is 13.

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