Question 330295

Start with the given system of equations:

{{{system(x+y=4,x-y=5)}}}



Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(x+y)+(x-y)=(4)+(5)}}}



{{{(x+x)+(y-y)=4+5}}} Group like terms.



{{{2x+0y=9}}} Combine like terms.



{{{2x=9}}} Simplify.



{{{x=(9)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



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{{{x+y=4}}} Now go back to the first equation.



{{{9/2+y=4}}} Plug in {{{x=9/2}}}.



{{{2(9/cross(2)+y)=2(4)}}} Multiply both sides by the LCD {{{2}}} to clear any fractions.



{{{9+2y=8}}} Distribute and multiply.



{{{2y=8-9}}} Subtract {{{9}}} from both sides.



{{{2y=-1}}} Combine like terms on the right side.



{{{y=(-1)/(2)}}} Divide both sides by {{{2}}} to isolate {{{y}}}.



So the solutions are {{{x=9/2}}} and {{{y=-1/2}}}.



Which form the ordered pair *[Tex \LARGE \left(\frac{9}{2},-\frac{1}{2}\right)].



This means that the system is consistent and independent.