Question

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?

Answer 1

The larger number = 8

Explanation:

Below is the system of equations:

y = -x + 10

y = 4x

Since both equations equal "y", we can set them equal to each other:

4x = -x + 10

4x + x = 10

5x = 10

x = 2

This means that at x = 2, the y-values of both equations are the same and is when the criteria of "the sum of two numbers are 10 and the larger number is 4 times the smaller number" is met

"x" is the smaller number. To find the bigger number, input "x" into either one of the equations in the system:

y = 4(2) = 8

Answer 2

he system of equations used to represent this scenario is y = –x + 10 and y = 4x, where x and y are the two numbers.

To find the larger number, we can solve the system of equations by setting y = 4x in the first equation and solving for x.

y = –x + 10

4x = –x + 10

3x = 10

x = 10/3

So the smaller number is 10/3. To find the larger number, we know that it is 4 times the smaller number, which is 4(10/3) = 40/3.

Therefore, the larger number is 40/3.