Question 175920
I'll do the first one to get you going in the right direction



# 1





Start with the given system of equations:

{{{system(x-2y=-1,-x+5y=4)}}}



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



{{{(x-2y)+(-x+5y)=(-1)+(4)}}}



{{{(x-x)+(-2y+5y)=-1+4}}} Group like terms.



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



{{{3y=3}}} Simplify.



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



{{{y=1}}} Reduce.



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{{{x-2y=-1}}} Now go back to the first equation.



{{{x-2(1)=-1}}} Plug in {{{y=1}}}.



{{{x-2=-1}}} Multiply.



{{{x=-1+2}}} Add {{{2}}} to both sides.



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



So our answer is {{{x=1}}} and {{{y=1}}}.



Which form the ordered pair *[Tex \LARGE \left(1,1\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(1,1\right)]. So this visually verifies our answer.



{{{drawing(500,500,-9,11,-9,11,
grid(1),
graph(500,500,-9,11,-9,11,(-1-x)/(-2),(4+x)/(5)),
circle(1,1,0.05),
circle(1,1,0.08),
circle(1,1,0.10)
)}}} Graph of {{{x-2y=-1}}} (red) and {{{-x+5y=4}}} (green)