Question 170659


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




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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=-9-2}}}Subtract 2 from both sides



{{{0=-11}}} Combine like terms on the right side



{{{0=-11}}} Simplify


Since this equation is <font size=4><b>NEVER</b></font> true for any x value, this means there are no solutions.



So the system is inconsistent.