You have a total of 21 pens and pencils. You have 3 more pens than pencils. Write a system of linear equations that represent this situation. How many of each do you have?

Let p = number of pencils

Therefore pens = p + 3

P + (p+3) = 21
2p + 3 = 21

Then solve for p

pens--- x

pencils --y
x+y = 21

x = y+3

I just translated the English to Math

solve

Let's denote the number of pens as "x" and the number of pencils as "y".

According to the information given, we know that you have a total of 21 pens and pencils. So the first equation would be:

x + y = 21

We also know that you have 3 more pens than pencils. This can be represented as:

x = y + 3

Now, we have a system of linear equations:

x + y = 21 ...(1)

x = y + 3 ...(2)

To find the number of pens and pencils, we can solve this system of equations.

To represent this situation using a system of linear equations, let's define two variables:

Let's say "x" represents the number of pencils you have.
Let's say "y" represents the number of pens you have.

According to the given information, you have a total of 21 pens and pencils:

x + y = 21 (Equation 1)

You also have 3 more pens than pencils:

y = x + 3 (Equation 2)

Now we have a system of linear equations representing the given situation. To find the values of x and y, we can solve this system.

To solve the system, we can use the substitution method or the elimination method. Let's use the substitution method:

From Equation 2, we can rewrite it as y - x = 3.

Now we can substitute this value of (y - x) in Equation 1:

(x + (y - x)) = 21

Simplifying this equation, we get:

y = 21

Therefore, the value of y is 21.

Now we can substitute this value of y in Equation 2:

21 - x = 3

By rearranging this equation, we can find the value of x:

x = 21 - 3 = 18

So, the number of pencils (x) is 18, and the number of pens (y) is 21.