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The sum of 2 numbers is 100. Twice the first number plus twice the second number is 200. What are the numbers?

Write a system of equations for this situation and solve using inspection. Please show work please I don’t understand this!!!!!

Sagot :

YourMomsBrainidn

Answer:

50+50=100

100+100=200

Step-by-step explanation:

The sum of 2 numbers is 100. 50 x 2 = 100

Twice the first number plus twice the second number is 200.

50+50=100 so therfore 100+100 makes 200

This situation has infinitely many solutions.

What is system of equation?

"A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously".

For the given situation,

Let us consider the numbers be [tex]x[/tex] and [tex]y[/tex].

So the system of equations are represented as

[tex]x+y=100[/tex] and

[tex]2x+2y=200[/tex]

We first express the value of [tex]x[/tex] in terms of [tex]y[/tex] from the equation [tex]x+y=100[/tex] as, [tex]x=100-y[/tex]

Now we substitute the value of [tex]x[/tex] in the second equation, we get

⇒[tex]2(100-y)+2y=200[/tex]

⇒[tex]200-2y+2y=200\\[/tex]

⇒[tex]200=200[/tex]

This statement is true for all values of y.

Hence, we could not conclude a single solution for the above situation. It has infinitely many solutions.

Learn more about system of equations here

https://brainly.com/question/20621135

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