SOLUTION: What is the value of the y variable in the solution to the following system of equations? 5x + 4y = 1 4x + 3y = -1

Algebra ->  Expressions-with-variables -> SOLUTION: What is the value of the y variable in the solution to the following system of equations? 5x + 4y = 1 4x + 3y = -1      Log On


   

Question 315322: What is the value of the y variable in the solution to the following system of equations?
5x + 4y = 1
4x + 3y = -1
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


system%285x+%2B+4y+=+1%2C%0D%0A4x+%2B+3y+=+-1%29



To make the y terms cancel out, multiply

the first equation through by -3 and the

second equation through by +4:







system%28-15x+-+12y+=+-3%2C%0D%0A%22%22%2B16x+%2B+12y+=+-4%29



Add those two equations vertically term by term and get:



x=-7



To make the x terms cancel out, multiply

the first equation through by -4 and the

second equation through by +5:







system%28-20x+-+16y+=+-4%2C%0D%0A%22%22%2B20x+%2B+15y+=+-5%29



Add those two equations vertically term by term and get:



-y=-9

y=9



The solution is (x,y) = (-7,9)



Checking:



system%285x+%2B+4y+=+1%2C%0D%0A4x+%2B+3y+=+-1%29



system%285%28-7%29+%2B+4%289%29+=+1%2C%0D%0A4%28-7%29+%2B+3%289%29+=+-1%29



system%28-35+%2B+36+=+1%2C%0D%0A-28+%2B+27+=+-1%29



system%281+=+1%2C%0D%0A-1+=+-1%29



The solutions check