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

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


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a linear system of equations by subsitution


%281%29%2Ax%2B%283%2F2%29%2Ay=-1 Start with the second equation


2%28%281%29%2Ax%2B%283%2F2%29%2Ay%29=%282%29%2A%28-1%29 Multiply both sides by the LCD 2



2%2Ax%2B3%2Ay=-2 Distribute and simplify


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



Lets start with the given system of linear equations

2%2Ax%2B3%2Ay=12
2%2Ax%2B3%2Ay=-2

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

3%2Ay=12-2%2AxSubtract 2%2Ax from both sides

y=%2812-2%2Ax%29%2F3 Divide both sides by 3.


Which breaks down and reduces to



y=4-%282%2F3%29%2Ax Now we've fully isolated y

Since y equals 4-%282%2F3%29%2Ax we can substitute the expression 4-%282%2F3%29%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


2%2Ax%2B3%2Ahighlight%28%284-%282%2F3%29%2Ax%29%29=-2 Replace y with 4-%282%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax%2B3%2A%284%29%2B3%28-2%2F3%29x=-2 Distribute 3 to 4-%282%2F3%29%2Ax

2%2Ax%2B12-%286%2F3%29%2Ax=-2 Multiply



2%2Ax%2B12-2%2Ax=-2 Reduce any fractions

2%2Ax-2%2Ax=-2-12 Subtract 12 from both sides


2%2Ax-2%2Ax=-14 Combine the terms on the right side



0%2Ax=-14 Now combine the terms on the left side.
0%2F1=-14%2F1 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 2%2Ax%2B3%2Ay=12 (red) and 2%2Ax%2B3%2Ay=-2 (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) About Me  (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.