The sum of two numbers is 43. One number is five less than three times the other number. What is the largest number?

31 is greater

Step-by-step explanation:

I will solve your system by substitution.

x=3y-5; 43=x+y

Step: Solve x=3y-5 for x:

Step: Substitute 3y-5for x in 43=x+y:

43=x+y

43=3y-5+y

43=4y-5 (Simplify both sides of the equation)

43+-4y=4y-5+-4y (Add - 4y to both sides)

-4y+43=-5

-4y+43+-43=-5+-43 (Add - 43 to both sides)

-4y=-48

(Divide both sides by - 4)

y=12

Step: Substitute12foryinx=3y-5:

x=3y-5

x = (3) (12) - 5

x=31 (Simplify both sides of the equation)

Answer:

x=31 and y=12

31 is greater than 12

31

Step-by-step explanation:

Let the numbers be x and y.

"The sum of two numbers is 43." gives us the first equation.

x + y = 43

"One number is five less than three times the other number." gives us the second equation.

y = 3x - 5

Now we solve the system of two equations below.

x + y = 43

y = 3x - 5

Since the second equation is already solved for y, we will use the substitution method. We substitute 3x - 5 for y in the first equation.

x + y = 43

x + 3x - 5 = 43

4x - 5 = 43

4x = 48

x = 12

The first number is 12. Now we find the second number.

x + y = 43

12 + y = 43

y = 31

The larger number is 31.