Question

A coordinate plane.
The sum of two numbers is 10. The larger number is 4 times the smaller number.

The system of equations used to represent this scenario is y = –x + 10 and y = 4x.
What is the larger number?
4
6
8
10

Answer 1

To find the larger number, we can solve the system of equations given:

1. \( y = -x + 10 \) (this represents the sum of the two numbers)
2. \( y = 4x \) (this represents the larger number being 4 times the smaller number)

We can set both equations equal to each other:

\[
4x = -x + 10
\]

Now, let's solve for \( x \):

1. Add \( x \) to both sides:
\[
4x + x = 10
\]
\[
5x = 10
\]

2. Divide by 5:
\[
x = 2
\]

Now that we have the value of the smaller number (\( x \)), we can find the larger number (\( y \)) using the equation \( y = 4x \):

\[
y = 4(2) = 8
\]

Therefore, the larger number is **8**.