SOLUTION: how do i use elemation to solve x+y=4 x+y=-7?

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Question 663008: how do i use elemation to solve x+y=4
x+y=-7?
Found 2 solutions by MathLover1, lynnlo:
Answer by MathLover1(20850) 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

1%2Ax%2B1%2Ay=4
1%2Ax%2B1%2Ay=-7

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 1 and 1 to some equal number, we could try to get them to the LCM.

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

1%2A%281%2Ax%2B1%2Ay%29=%284%29%2A1 Multiply the top equation (both sides) by 1
-1%2A%281%2Ax%2B1%2Ay%29=%28-7%29%2A-1 Multiply the bottom equation (both sides) by -1


So after multiplying we get this:
1%2Ax%2B1%2Ay=4
-1%2Ax-1%2Ay=7

Notice how 1 and -1 and 4 and -1 add to zero (ie 1%2B-1=0 1%2B-1=0)

However 4 and 7 add to 11 (ie 4%2B7=11);


So we're left with

0=11


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

Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
can't be solved ,it is inconsistent