Question 196630
Start with the given system of equations:

{{{system(2x+y=7,x-y=2)}}}



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



{{{(2x+y)+(x-y)=(7)+(2)}}}



{{{(2x+x)+(y-y)=7+2}}} Group like terms.



{{{3x+0y=9}}} Combine like terms. Notice how the "y" terms cancel out.



{{{3x=9}}} Simplify.



{{{x=(9)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



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{{{2x+y=7}}} Now go back to the first equation.



{{{2(3)+y=7}}} Plug in {{{x=3}}}.



{{{6+y=7}}} Multiply.



{{{y=7-6}}} Subtract {{{6}}} from both sides.



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



So the solutions are {{{x=3}}} and {{{y=1}}}.



Which form the ordered pair *[Tex \LARGE \left(3,1\right)].



This means that the system is consistent and independent.



Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(3,1\right)]. So this visually verifies our answer.



{{{drawing(500,500,-7,13,-9,11,
grid(1),
graph(500,500,-7,13,-9,11,7-2x,(2-x)/(-1)),
circle(3,1,0.05),
circle(3,1,0.08),
circle(3,1,0.10)
)}}} Graph of {{{2x+y=7}}} (red) and {{{x-y=2}}} (green)