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2015-10-16T15:50:43+08:00

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Let x be the smaller number and be the larger number. Then,
x + y = 19
2x + 3y = 48

First equation can be transformed as x = 19 - y.

Substituting this value to the second equation, we have
2(19 - y) + 3y = 48
38 - 2y + 3y = 48
38 + y = 48
y = 48 - 38
y = 10

Substituting the value of y to either of the two equations, we have
x + y = 19
x + 10 = 19
x = 19 - 10
x = 9

The two numbers are 9 and 10.

- D.E.


1 1 1
"...and y be the larger number". I will not post my answer for points, because I'd solve the problem the same way you did :-) :-)
Great Job! I did Gauss Jordan Method and it ... is not ... well as yours!
2015-10-17T11:15:03+08:00
Let x be the first number. It is the smaller number.
Let y be the second number. It is the larger number.

x + y = 19
2x + 3y = 48

Using Gaussian Elimination Method:
  \left[\begin{array}{ccc}1&1&19\\2&3&48\\\end{array}\right] 
 R1(2) - R2 = R2
  \left[\begin{array}{ccc}1&1&19\\0&-1&-10\\\end{array}\right] 
 R2(-1)
  \left[\begin{array}{ccc}1&1&19\\0&1&10\\\end{array}\right]
 \\ R1 - R2 = R1   \left[\begin{array}{ccc}1&0&9\\0&1&10\\\end{array}\right]



So therefore, the numbers are 9 and 10.

Check:
9 + 10 = 19
2(9) + 3(10) = 48
18 + 30 = 48
48 = 48
0
Gauss' method is cool :-)
Hahaha :-)