Question 50291This question is from textbook Beginning Algebra
: I am trying to solve the following system by using addition or substitution. If a unique solution does not exist, state whether the system is dependent or inconsistent.
I am unable to work this out. Can someone please help me?
10x+2y=7
y=-5x+3
This question is from textbook Beginning Algebra
Found 2 solutions by junior403, jackytavares:
Answer by junior403(76)   (Show Source):
You can put this solution on YOUR website! 10x+2y=7
y=-5x+3
We can solve this system of equations using the elimination method.
But first we need to put each equation in standard form so that they look the same. You have...
10x + 2y = 7
y = -5x + 3
The top equation is already in standard form so we just need to get the -5x in the bottom equation on the left side by adding it from both sides.
10x + 2y = 7
5x + y = 3
Now we are ready to begin eliminating variables.
First we need to decide which coefficiant to work with in order to cancel out or "eliminate" the other.
For instance, we have 10x and 5x.
What do we need to do to the 5x in order to cancel out the 10x?
What if we multiply the second (bottom) equation by -2?
10x + 2y = 7
-2(5x + y = 3)
When we distribute, we get...
10x + 2y = 7
-10x - 2y = -6
Now we can add our system to solve the equation. Like so...
10x + 2y = 7
-10x - 2y = -6
_______________
0 = 1
Is this statement true 0 = 1?
NO!
So the solution is inconsistent.
We can write the answer as...
zero, 0 or empty set, { }.
I hope this helps.
Good Luck!
Answer by jackytavares(5)  (Show Source):
You can put this solution on YOUR website! 10x+2y=7
y=-5x+3
We can solve this system of equations using the elimination method.
But first we need to put each equation in standard form so that they look the same. You have...
10x + 2y = 7
y = -5x + 3
The top equation is already in standard form so we just need to get the -5x in the bottom equation on the left side by adding it from both sides.
10x + 2y = 7
5x + y = 3
Now we are ready to begin eliminating variables.
First we need to decide which coefficiant to work with in order to cancel out or "eliminate" the other.
For instance, we have 10x and 5x.
What do we need to do to the 5x in order to cancel out the 10x?
What if we multiply the second (bottom) equation by -2?
10x + 2y = 7
-2(5x + y = 3)
When we distribute, we get...
10x + 2y = 7
-10x - 2y = -6
Now we can add our system to solve the equation. Like so...
10x + 2y = 7
-10x - 2y = -6
We can write the answer as...
zero, 0 or empty set, { }.
I hope this helps.
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