SOLUTION: Solve the system of equations by the addition method. -4x+y= -13 8x-2y= 2 The solution is? (Type an ordered pair. Type N if there is no solution. Type I if there

Algebra ->  Systems-of-equations -> SOLUTION: Solve the system of equations by the addition method. -4x+y= -13 8x-2y= 2 The solution is? (Type an ordered pair. Type N if there is no solution. Type I if there       Log On


   

Question 114021: Solve the system of equations by the addition method.
-4x+y= -13

8x-2y= 2

The solution is?
(Type an ordered pair. Type N if there is no solution. Type I if there are infinitely many solutions.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition


Lets start with the given system of linear equations

-4%2Ax%2B1%2Ay=-13
8%2Ax-2%2Ay=2

In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).

So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.

So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get -4 and 8 to some equal number, we could try to get them to the LCM.

Since the LCM of -4 and 8 is -8, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by 1 like this:

2%2A%28-4%2Ax%2B1%2Ay%29=%28-13%29%2A2 Multiply the top equation (both sides) by 2
1%2A%288%2Ax-2%2Ay%29=%282%29%2A1 Multiply the bottom equation (both sides) by 1


So after multiplying we get this:
-8%2Ax%2B2%2Ay=-26
8%2Ax-2%2Ay=2

Notice how -8 and 8 and -26 and -2 add to zero (ie -8%2B8=0 2%2B-2=0)

However -26 and 2 add to -24 (ie -26%2B2=-24);


So we're left with

0=-24


which means no value of x or y value will satisfy the system of equations. So there are no solutions


So this system is inconsistent