The sum of three numbers is 10. The sum of twice the first number, 3 times the second number, and 4 times the third number is 27. The difference between 7 times the first number and the second number is 23. Find the three numbers
first number:
second number:
third number:

Answer

Expert–verified

Hide Steps

Answer

The solution to the system of equations is $(3, 1, 6)$ .

Steps

Step 1 ：We have a system of three equations that we can solve using linear algebra. The equations are: $x + y + z = 10$ , $2 x + 3 y + 4 z = 27$ , and $7 x - y = 23$ .

Step 2 ：We can represent these equations in matrix form as: $[\begin{matrix} 1 & 1 & 1 \\ 2 & 3 & 4 \\ 7 & - 1 & 0 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] = [\begin{matrix} 10 \\ 27 \\ 23 \end{matrix}]$

Step 3 ：We can solve this system of equations using linear algebra.

Step 4 ：The solution to the system of equations is $(3, 1, 6)$ .

The sum of three numbers is 10. The sum of twice the first number, 3 times the second number, and 4 times the third number is 27. The difference between 7 times the first number and the second number is 23. Find the three numbersfirst number:second number:third number:

Answer

Popular Problems

The sum of three numbers is 10. The sum of twice the first number, 3 times the second number, and 4 times the third number is 27. The difference between 7 times the first number and the second number is 23. Find the three numbers
first number:
second number:
third number: