SOLUTION: Set up a system of linear equations and solve for the indicated quantities. Three times the smaller of two numbers plus 2 times the larger number is 27. Four times the smaller numb

Algebra ->  Linear-equations -> SOLUTION: Set up a system of linear equations and solve for the indicated quantities. Three times the smaller of two numbers plus 2 times the larger number is 27. Four times the smaller numb      Log On


   

Question 1124231: Set up a system of linear equations and solve for the indicated quantities. Three times the smaller of two numbers plus 2 times the larger number is 27. Four times the smaller number minus 2 times the larger number is -6. Find the numbers
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Follow the description exactly. You can decide how to assign variable or variables to what.

x, smaller number
y, larger number

system%283x%2B2y=27%2C4x-2y=-6%29
You can solve that system.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the smaller and y be the greater number.


Then your system is


3x + 2y = 27,    (1)
4x - 2y = -6.    (2)


To solve it, add the equations (both sides).  You will get

3x + 4x = 27 - 6,    or

7x = 21  ====>    x = 21/7 = 3.


Then from eq(1),  2y = 27 - 3x = 27 - 3*3 = 18  and  y = 18/2 = 9.


Answer.  The smaller number is 3.  The greater number is 9.