write a system of equations modeling the given conditions. then solve the system by the substitution method and find the two numbers

Question

write a system of equations modeling the given conditions. then solve the system by the substitution method and find the two numbers. the difference between two numbers is 3. the sum of the larger number and four times the smaller number is 23. find the numbers

Answer 1

Hi, Cheyenne.

 

Let the numbers be:

X, Y

 

Let Y be the larger number.

 

Y - X = 3

Y + 4X = 23

 

Now, you can solve for Y from the first equation:

Y = 3 + X

 

Then, you substitute the value for Y into the 2nd equation:

3 + X + 4X = 23

3 + 5X = 23

5X = 20

X = 4

 

So, the smaller number is 4.

The larger number is Y = 3 + X so

Y = 7

 

So the numbers are 4, 7