Expert: Richard J. Raridon - 12/1/2008

Question
QUESTION: I was ask to write a system of equations for the following questions and I responded with the following answers.  Are these correct?  Thank you.
a.   A unique solution. X+3y=15 and 2x+15y=10  a1/a2= ½  b1/b2=1/3 the numbers don’t equal each other so it is unique
b.   An infinite number of solutions. X+4y=8 and 3x+12y=24  a1/a2=1/3 b1/b2=1/3 c1/c2=1/3 they are all equal so it is infinite
c.   No solution. 2x+3y=4 and 4x+6y=9   a1/a2= ½  b1/b2= ½  c1/c2=4/9  therefore there is no solution




ANSWER: you are correct.  
b. those are really the same equation
c. those lines are parallel and so they never cross

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

QUESTION: If I may could you provide me with feedback to this problem.

Thanks


5.   Explain how to apply elimination in solving a system of equations. In elimination you would add the two equations together by eliminating either the x or y term. 3x+9y=12 and 5x-4y=3 ;  5(3x+9y=12)   -3(5x-4y=3);   (15x+45y=60)+(-15x+12y=-9)   57y=51  y=51/57; y=17/19 3x+9(51/57)=12; 3x+459/57=12; 3x=12-(459/57);  3x=(684/57)-(459/57); 3x=225/57; x=(225/57)/3;  x= (225/57)(1/3); x=75/57 ;  x=25/19  

Answer
You got the right answer but you went through a lot more steps than I would have.  First of all, I would have divided by 3 to get
x+3y = 4. So then if you mult. by 4 to get 4x+12y=16 and mult. the other by 3 to get 15x-12y = 9, and add them together you get 19x=25.