Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 170659This question is from textbook Introductory Algebra
: Solve by the substitution method
x + y = 2
x + y = -9This question is from textbook Introductory Algebra
: Solve by the substitution method
x + y = 2
x + y = -9
Answer by jim_thompson5910(9921) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

system(x+y=2,x+y=-9)



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

x+y=2 Start with the first equation


y=2-x Subtract x from both sides


y=-x+2 Rearrange the equation



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

Since y=-x+2, we can now replace each y in the second equation with -x+2 to solve for x



x+highlight((-x+2))=-9 Plug in y=-x+2 into the second equation. In other words, replace each y with -x+2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2=-9 Combine like terms on the left side


0=-9-2Subtract 2 from both sides


0=-11 Combine like terms on the right side


0=-11 Simplify

Since this equation is NEVER true for any x value, this means there are no solutions.


So the system is inconsistent.