A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situat…

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asked Sep 5, 2019 222k views

2 Answers

Pranay Kumar · Answer 1 · 2019-09-09T12:28:49+0000

Answer:

The following system represents the situation :

$\left \{ {{y=2(x+3)} \atop {y=5+3x}} \right.$

And the solution is
(x,y)=(1,8)

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 :

y=2(x+3) (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 :

y=5+3x (II)

Now we can make our system we equations (I) and (II) :

$\left \{ {{y=2(x+3)} \atop {y=5+3x}} \right.$

If we want to solve the system, we can use the equation (II) in the equation (I) :

5+3x=2(x+3)

5+3x=2x+6

x=1 ⇒ Using x = 1 in (I) or (II) ⇒

y=2(x+3)

y=2(1+3)

y=2.(4)

y=8