SOLUTION: Solve the following system by substitution 4x-12y=5, -x+3y= -1 Show your solution below: What is the solution for this system? What type of system is this?

Question 124876: Solve the following system by substitution
4x-12y=5,
-x+3y= -1
Show your solution below:
What is the solution for this system?
What type of system is this?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

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

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Multiply both sides by the LCM of 12. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)

Distribute and multiply the LCM to each side

Combine like terms on the left side

Add 15 to both sides

Combine like terms on the right side

Since this equation is never true for any x value, this means there are no solutions. So the system is inconsistent.

RELATED QUESTIONS
Please help. I don't understand this. Solve the following system by substitution. If a... (answered by funmath)

. Solve the following system by substitution. 4x � 12y = 5 -x + 3y = -1 (answered by Cintchr)

solve the following system by substitution. 4x -12y= 5 -x +3y=-1 (answered by venugopalramana)

Solve the following system by substitution 4x-12y=5 -x+3y=-1 (answered by jessbear13)

Please help. Solve the following system by substitution. 4x - 12y = 5 -x + 3y = (answered by MathLover1)

Solve the following system by substitution 4x-12y=5 -x+3y=-1 (answered by jim_thompson5910)

Solve the following system by substitution 8x-4y=16 y=2x-4 Show your solution... (answered by stanbon)

Solve the system by addition. If solution does not exist, state whether the system is... (answered by iluvbuilding429)

solve system by substitution 4x-12y= 5 -x+... (answered by jim_thompson5910)