SOLUTION: three times the first number decreased by a second number is 8. the first number decreased by twice the second number is 19. whats the first number and the second number?

Question 421687: three times the first number decreased by a second number is 8. the first number decreased by twice the second number is 19.
whats the first number and the second number?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = the 1st number
let y = the 2nd number
:
write an equation for each statement. We will use substitution here.
:
three times the first number decreased by a second number is 8.
3x - y = 8
-y = -3x + 8
Multiply by -1
y = 3x - 8
:
the first number decreased by twice the second number is 19.
x - 2y = 19
Replace y with (3x-8)
x - 2(3x-8) = 19
x - 6x + 16 = 19
-5x = 19 - 16
-5x = 3
x =
x = -.6
:
Find y using: y = 3x - 8
y = 3(-.6) - 8
y = -1.8 - 8
y = -9.8
:
:
Check solution in the 1st equation
3x - y = 8
3(-.6) - (-9.8)
-1.8 + 9.8 = 8; confirms our solution of x=-.7; y=-9.8

whats the first number and the second number?
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