Question 236583


Start with the given system of equations:

{{{system(x+9y=66,-x+9y=60)}}}



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



{{{(x+9y)+(-1x+9y)=(66)+(60)}}}



{{{(1x+-1x)+(9y+9y)=66+60}}} Group like terms.



{{{0x+18y=126}}} Combine like terms.



{{{18y=126}}} Simplify.



{{{y=(126)/(18)}}} Divide both sides by {{{18}}} to isolate {{{y}}}.



{{{y=7}}} Reduce.



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{{{x+9y=66}}} Now go back to the first equation.



{{{x+9(7)=66}}} Plug in {{{y=7}}}.



{{{x+63=66}}} Multiply.



{{{x=66-63}}} Subtract {{{63}}} from both sides.



{{{x=3}}} Combine like terms on the right side.



So the solutions are {{{x=3}}} and {{{y=7}}}.



Which form the ordered pair *[Tex \LARGE \left(3,7\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(3,7\right)]. So this visually verifies our answer.



{{{drawing(500,500,-7,13,-3,17,
grid(1),
graph(500,500,-7,13,-3,17,(66-x)/(9),(60+x)/(9)),
circle(3,7,0.05),
circle(3,7,0.08),
circle(3,7,0.10)
)}}} Graph of {{{x+9y=66}}} (red) and {{{-x+9y=60}}} (green)