Question 227223
Three numbers, x, y, z
:
Write an equation for each statement:
:
"the sum of three numbers is -2."
x + y + z = -2
:
"the sum of three times the first number, twice the second number, and the third number is 9."
3x + 2y + z = 9
:
" the difference between the second number and half the third number is 10."
y - .5z = 10
:
find the numbers:
:
Multiply the last equation by 2 and add to the 1st equation
x + y + z = -2
0 + 2y -z = 20
---------------addition eliminates z
x + 3y = 18
:
Add the same equation to the 2nd the equation
3x + 2y + z = 9
0 + 2y  - z = 20
------------------eliminate z again
3x + 4y = 29
:
Use these two 2 unknown equations to eliminate x
Multiply the 1st one by 3
3x + 9y = 54
3x + 4y = 29
--------------Subtraction eliminates x
0x + 5y = 25
y = {{{25/5}}}
y = 5
:
Using y - .5z = 10
5 - .5z = 10
-.5z = 10 - 5
z = {{{5/(-.5)}}}
z= -10
:
Find x using the 1st equation
x + 5 -10 = -2
x - 5 = -2
x = - 2 + 5
x = +3
:
:
Check solutions in the 2nd equation
3x + 2y + z = 9
3(3) + 2(5) - 10 = 9; confirms our solution