Expert: Richard J. Raridon - 3/10/2009

Question
QUESTION: Richard,

can you show me how to do these questions?

1.   Solve by substitution or elimination method:
      3x minus 2y equals 26
      -7x plus 3y equals -49

2. 4x minus 5y equals 14
 -12x plus 15y equals -42

3. -2x plus 6y equals 19
10x  minus 30y equals -15


ANSWER: 1. 3x -2y = 26 and -7x +3y = -49 so x = 4, y = -7
2. 4x -5y = 14 and -12x +15y = -42 so no solution, lines are identical
3. -2x +6y = 19 and 10x -30y = -15 so no solution, lines are parallel

---------- FOLLOW-UP ----------

QUESTION: Richard,

I have been trying to fiqure out how you got the answers, but I can't tell what steps you use.  I get totally different answers than you.


Answer
Haven't you learned how to solve two equations, two unknowns?        1. multiply 1st eq. by 3 to get 9x -6y = 78
multiply 2nd eq. by 2 to get -14x+6y = -98
add these equations to get -5x = -20 so x = 4 and then y = -7
You can put these answers back into both original equations and see that they are correct.  
2. Divide the 2nd eq. by -3 and you get 4x -5y = 14, identical to the 1st eq.  
3. divide the 2nd eq. by -5 and you get -2x +6y = 3
so the two lines are parallel and never cross.