SOLUTION: Solve by addition or subtraction. If a unique solution does not exist, state whether the system is dependant or independent. 10x+2y=7 y=-5x+3

Question 108989: Solve by addition or subtraction. If a unique solution does not exist, state whether the system is dependant or independent.
10x+2y=7
y=-5x+3
Answer by mrkoje(1) (Show Source): You can put this solution on YOUR website!
Hello.
Eq (1) 10x + 2y = 7
Eq (2) y = -5x + 3

Notice that if we add 5x to both sides of equation (2) we will get:
5x + y = 3

Now forming our modified system of equations we get:

10x + 2y = 7
5x + y = 3
Now here is the important part. To solve by addition or subtraction we will need to multiply Eq (2) by a some number that will let us clear out the "x" variable.
Here is what to do:
Step 1. Multiply Eq (2) that is 2 * (5x + y = 3 ) which should give us 10x + 2y = 6.
Step 2. Now we can subtract Eq (2) from (1).

10x + 2y = 7
- 10x + 2y = 6
_______________
0x + 0y = 1
(which is inconsistent since zero of something clearly can not equal one of something.)
Another way to look at the problem is with substitution.
For example in the original system:
10x + 2y = 7
y = -5x +3
The second equation is already solved for the variable "y." We could just simply substitute that equation for the instance of Y in the first equation
10x + 2(-5x+3) = 7
Which expands to:
10x -10x + 6 = 7
And that simplifies to:
6 = 7 (which is clearly not true) So we can see that the system in inconsistent.

Finally, a unique solution to this system is impossible.

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