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 ->  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 102924: 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 Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1. 10%2Ax%2B2y=7
2. y=-5%2Ax%2B3
Use equation (2) and substitute into (1):
2.y=-5%2Ax%2B3
2%2Ay=2%2A%28-5%2Ax%2B3%29
2%2Ay=2%2A%28-5%2Ax%29%2B2%2A3 Distributive property.
2%2Ay=-10%2Ax%2B6 Simplify.
2%2Ay%2B10%2Ax=cross%28-10%2Ax%29%2Bcross%2810%2Ax%29%2B6 Additive inverse of (-10*x).2%2Ay%2B10%2Ax=6 Simplify.
cross%282%2Ay%29-cross%282%2Ay%29%2B10%2Ax=6-2%2AyAdditive inverse of (2*y).
10%2Ax=6-2%2AySimplify.
Use this results in equation (1).
1. 10%2Ax%2B2y=7
6-cross%282%2Ay%29%2Bcross%282y%29=7
6=7
Since the equations lead to a false statement, they are inconsistent.
+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+-5x%2B3%2C-5x%2B3.5%29+
Looking at the graphs of both equations, you see that they have the same slope (parallel) and different intercepts. They will never meet (i.e. have a solution).