SOLUTION: Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent. 10x + 2y

Algebra ->  Linear-equations -> SOLUTION: Solve each of the following systems by using either addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent. 10x + 2y      Log On


   

Question 74960: Solve each of the following systems by using either addition or substitution. If a unique solution
does not exist, state whether the system is dependent or inconsistent.
10x + 2y = 7
y = -5x + 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to use substitution since we already have y isolated
10x+%2B+2y+=+7
y+=+-5x+%2B+3Plug this into y for the 1st equation
10x+%2B+2%28-5x%2B3%29+=+7
10x+-10x%2B6+=+7Distribute the 2
6+=+7Add like terms. Since this equation is false, there are no solutions. If you solved the 1st equation for y, you would get:
y=-5x%2B7%2F2 Since this equation has the same slope as y+=+-5x+%2B+3
these two lines are parallel and will never cross. So this system is inconsistent
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-5x+%2B+3%2C+-5x%2B7%2F2%29+ Graph of y+=+-5x+%2B+3 and y=-5x%2B7%2F2