Answer:
The following system represents the situation :
[tex]\left \{ {{y=2(x+3)} \atop {y=5+3x}} \right.[/tex]
And the solution is [tex](x,y)=(1,8)[/tex]
Step-by-step explanation:
In order to write the equations that represent the situation we need to read carefully the question.
The first sentence is : '' A number, y, is equal to twice the sum of a smaller number and 3.''
We define the following variables :
y : '' The largest number ''
x : '' The smallest number ''
From the first sentence we can write the first equation of the system :
[tex]y=2(x+3)[/tex] (I)
The second sentence is : '' The larger number is also equal to 5 more than 3 times the smaller number. ''
From this sentence we can write :
[tex]y=5+3x[/tex] (II)
Now we can make our system we equations (I) and (II) :
[tex]\left \{ {{y=2(x+3)} \atop {y=5+3x}} \right.[/tex]
If we want to solve the system, we can use the equation (II) in the equation (I) :
[tex]5+3x=2(x+3)[/tex]
[tex]5+3x=2x+6[/tex]
[tex]x=1[/tex] ⇒ Using x = 1 in (I) or (II) ⇒
[tex]y=2(x+3)[/tex]
[tex]y=2(1+3)[/tex]
[tex]y=2.(4)[/tex]
[tex]y=8[/tex]
