SOLUTION: Which system of equations has no solution? 3x+6y=-6 3x-6y=-6 3x+6y=-6 9x+18y=-18 3x+6y=-6 3x+6y=-7 3x+6y=-6 5x-4y+-7

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Question 105731: Which system of equations has no solution?
3x+6y=-6
3x-6y=-6
3x+6y=-6
9x+18y=-18
3x+6y=-6
3x+6y=-7
3x+6y=-6
5x-4y+-7
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

2.


there are no solutions, and the system is
the system is that the equations have the same slope and the same intercept, and the lines are actually both the same line
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations




Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

Subtract from both sides

Divide both sides by 6.


Which breaks down and reduces to



Now we've fully isolated y

Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x.


Replace y with . Since this eliminates y, we can now solve for x.

Distribute 18 to

Multiply



Reduce any fractions

Add to both sides


Combine the terms on the right side



Now combine the terms on the left side.
Since this expression is true for any x, we have an identity.


So there are an infinite number solutions. The simple reason is the 2 equations represent 2 lines that overlap each other. So they intersect each other at an infinite number of points.

If we graph and we get

graph of


graph of (hint: you may have to solve for y to graph these)

we can see that these two lines are the same. So this system is dependent



3.


there are no solutions, and the system is

Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations




Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

Subtract from both sides

Divide both sides by 6.


Which breaks down and reduces to



Now we've fully isolated y

Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x.


Replace y with . Since this eliminates y, we can now solve for x.

Distribute 6 to

Multiply



Reduce any fractions

Add to both sides


Combine the terms on the right side



Now combine the terms on the left side.
Since this expression is not true, we have an inconsistency.


So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist.


graph of (red) and (green) (hint: you may have to solve for y to graph these)


and we can see that the two equations are parallel and will never intersect. So this system is inconsistent
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