SOLUTION: Could you please help me with a question? Solve the system: 2x + 3y = 12 x + 1.5y = -1

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Question 91149: Could you please help me with a question?
Solve the system:
2x + 3y = 12
x + 1.5y = -1
Found 2 solutions by jim_thompson5910, checkley71:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


Start with the second equation


Multiply both sides by the LCD 2



Distribute and simplify


-----------------------------------------



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 3.


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 3 to

Multiply



Reduce any fractions

Subtract from 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
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
2X+3Y=12 OR 3Y=-2X+12 OR Y=-2X/3+12/3 OR Y=-2X/3+4 (RED LINE)
X+1.5Y=-1 OR 1.5Y=-X-1 OR Y=-X/1.5-1/1.5 (GREEN LINE)
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = -2x/3 +4 and y = -x/1.5 -1/1.5).
SEEING AS THESE ARE PARALLEL LINES THERE IS NO UNIQUE SOLUTION TO THESE TWO EQUATIONS.
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