# College algebra

posted by .

system of linear equation

The sum of 3 numbers is 14
the largest is 4 times the smallest
the sum of the smallest and twice the largest is 18
what are the 3 numbers? show work?

A. how many unknowns you have?
-how many equations need to be solve for that many unknown?

B. what are the equations?

C. used the system of equations using matrices.

• College algebra -

x+y+z=14
z=4x
x+2z=18
=================
x+y+4x = 14 or 5x+y = 14
x+8x = 18
or x = 2
so
y = 14 - 10 = 4
z = 4*2=8
3 unknowns, three equations
I did it with substitution, however can form augmented matrix and use Gauss Jordan:
+1 1 1 14
-4 0 1 0
+1 0 2 18

then plug and chug

• College algebra -

post it.

• College algebra -

matix solution
|1 1 1 | [x y z]'= [14 0 18]'
|4 0 1 |
|1 0 2 |

H*[x y z]' = [14 0 18]' (' stands for transpose; in this case makes row vector a column vector)

inv(H)*H*[x y z]'= inv(H)*[14 0 18]'

[x y z] = inv(H)*[14 0 18]'

inverting a 3x3 matrix

|+(0-0) -(-8-1) +(0-0)|'
|-(2-0) -(2-1) -(0-1)|
|+(1-0) -(1+4) +(0+4)|

|0 9 0|'
|-2 -1 1|
|1 -5 4|

=|0 -2 1|
|9 -1 -5|
|0 1 4|

det(H)= use the second column
since it has 2 zeros it makes
it easy.

det(H)=-1(-8-1)+0*(2-1)-0*(1+4)=9

inv(H)=1/9*|0 -2 1|
|9 -1 -5|
|0 1 4|

[x y z]'= inv(H)*[14 0 18]'

=[18/9 (9*14-5*18)/9 (18*4)/9]'
=[ 2 4 8 ]'

hope this helps

## Similar Questions

1. ### Algebra

The measure of the largest angle of a certain triangle is 6 times the smallest. The measure of the remaining angle is 100 degrees less than te sum of the other two angles. Write a system of 3 equations you could use to solve this problem. …
2. ### Integers

Suppose a1, a2, . . . , an is a list of n numbers with the following properties: The sum of those n numbers is 500. The sum of the smallest three of those numbers is 48. The sum of the largest two of those numbers is 35. (Note: There …
3. ### algebra 2

three numbers in the ratio of 7:3:2 have a sum of 228. what is the difference between the smallest and the largest numbers?
4. ### MATH

system of linear equation The sum of 3 numbers is 14 the largest is 4 times the smallest the sum of the smallest and twice the largest is 18 what are the 3 numbers?
5. ### Algebra

3 real numbers that form a geometric progression have sum equal to 175 and product equal to 17576. What is the sum of the largest and smallest numbers?
6. ### Algebra

3 real numbers that form a geometric progression have sum equal to 175 and product equal to 17576. What is the sum of the largest and smallest numbers?
7. ### algebra

Identify the vertices of the solution region of the system of linear inequalities. (Order your answers from smallest to largest x, then from smallest to largest y.) x ≥ −2 x ≤ 3 y ≤ 5 y ≥ x (x, y) = (x, …
8. ### algebra

The sum of 3 numbers is 24. Twice the smallest number is 2 less than the largest number and the largest number is equal to the sum of the other two. what are the three numbers?
9. ### college algebra

Three even numbers sum up to 104. The smallest is half the largest and the middle number is 2 3 the largest. What are the three numbers?
10. ### College Alebra

Solve the following using system of equations. The sum of three numbers is 26. The middle number numerically is one more than three times the smallest number. The largest number is two times less than five times the smallest number. …

More Similar Questions