SOLUTION: please help me solve this linear system ( Three times one number increased by twice a second number is 29. Four times the first less three times the second is 16. Find the numbers

Question 344117: please help me solve this linear system ( Three times one number increased by twice a second number is 29. Four times the first less three times the second is 16. Find the numbers
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
( Three times one number increased by twice a second number is 29. Four times the first less three times the second is 16. Find the numbers
:
Two numbers, x & y
:
Write an equation for each statement
:
"Three times one number increased by twice a second number is 29."
3x + 2y = 29
:
"Four times the first less three times the second is 16."
4x - 3y = 16
:
We can use elimination here,
Multiply the 1st equation by 3, multiply the 2nd equation by 2,
9x + 6y = 87
8x - 6y = 32
---------------addition eliminates y, find x
17x = 119
x =
x = 7
:
Find y using the 1st equation, replace x with 7
3(7) + 2y = 29
21 + 2y = 29
2y = 29 - 21
2y = 8
y = 4
:
:
Check solutions in the 2nd equation
4x - 3y = 16
4(7) - 3(4) = 16
28 - 12 = 16; confirms our solution of x=7, y=4
:
:
How about this, did this make sense to you?

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