SOLUTION: Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistaent or dependent: 2x+3y=1 5x+3y=16

Algebra ->  Systems-of-equations -> SOLUTION: Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistaent or dependent: 2x+3y=1 5x+3y=16      Log On


   

Question 82041: Solve the following system by addition. If a unique solution does not exist, state whether the system is inconsistaent or dependent:
2x+3y=1
5x+3y=16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Linear Systems by Addition
We'll solve the system:
2%2Ax+%2B+3%2Ay+=+1
5%2Ax+%2B+3%2Ay+=+16
by elimination by addition.To eliminate by addition, we need to set both coefficients of x to numbers with changed signs, i.e a and -a. Since in the second equation we have 5 as our coefficient for x, to get -2 we have to multiply all terms of the second equation by -2%2F5 which is equal to -0.4.

Multiplying, we get on our second equation:%285%2A-0.4%29x+%2B+%283%2A-0.4%29y+=+16%2A-0.4
-2%2Ax+%2B+-1.2%2Ay+=+-6.4

Adding both equations we get:

%282%2B-2%29x+%2B+%283%2B-1.2%29y+=+%281%2B-6.4%29

Since 2 and -2 cancel out, we have a linear equation:Therefore, we know that y = -3.

Plugging that in into the first equation gives us:

2%2Ax+%2B+3%2Ay+=+1
2%2Ax+%2B+3%2A-3+=+1
2%2Ax+%2B+-9+=+1
2%2Ax+=+1+-+-9
x+=+%281+-+-9%29%2F2
x+=+10%2F2
x+=+5

Therefore, our answer is:

system%28+x=5%2C+y=-3+%29