SOLUTION: The question I have ben posed is to: solve the system for 2x+3=12 x+1.5y=-1 I know this may be asy for some but not for me. Thank you nevrstndstil@yahoo.com

Algebra ->  Expressions-with-variables -> SOLUTION: The question I have ben posed is to: solve the system for 2x+3=12 x+1.5y=-1 I know this may be asy for some but not for me. Thank you nevrstndstil@yahoo.com      Log On


   

Question 90527: The question I have ben posed is to:
solve the system for
2x+3=12
x+1.5y=-1
I know this may be asy for some but not for me.
Thank you
nevrstndstil@yahoo.com
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B3y=12
10%28x%2B1.5y%29=10%28-1%29 Multiply both sides by 10


2x%2B3y=12
10x%2B15y=-10

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


Lets start with the given system of linear equations

2%2Ax%2B3%2Ay=12
10%2Ax%2B15%2Ay=-10

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.


10%2Ax%2B15%2Ahighlight%28%284-%282%2F3%29%2Ax%29%29=-10 Replace y with 4-%282%2F3%29%2Ax. Since this eliminates y, we can now solve for x.

10%2Ax%2B15%2A%284%29%2B15%28-2%2F3%29x=-10 Distribute 15 to 4-%282%2F3%29%2Ax

10%2Ax%2B60-%2830%2F3%29%2Ax=-10 Multiply



10%2Ax%2B60-10%2Ax=-10 Reduce any fractions

10%2Ax-10%2Ax=-10-60 Subtract 60 from both sides


10%2Ax-10%2Ax=-70 Combine the terms on the right side



0%2Ax=-70 Now combine the terms on the left side.
0%2F1=-70%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 10%2Ax%2B15%2Ay=-10 (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