Question 195945
I'll do the two problems to get you started


A)





Start with the given system of equations:

{{{system(3x-y=3,3x+y=15)}}}



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



{{{(3x-y)+(3x+y)=(3)+(15)}}}



{{{(3x+3x)+(-y+y)=3+15}}} Group like terms.



{{{6x+0y=18}}} Combine like terms.



{{{6x=18}}} Simplify.



{{{x=(18)/(6)}}} Divide both sides by {{{6}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



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{{{3x-y=3}}} Now go back to the first equation.



{{{3(3)-y=3}}} Plug in {{{x=3}}}.



{{{9-y=3}}} Multiply.



{{{-y=3-9}}} Subtract {{{9}}} from both sides.



{{{-y=-6}}} Combine like terms on the right side.



{{{y=(-6)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{y}}}.



{{{y=6}}} Reduce.



So the solutions are {{{x=3}}} and {{{y=6}}}.



Which form the ordered pair *[Tex \LARGE \left(3,6\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(3,6\right)]. So this visually verifies our answer.



{{{drawing(500,500,-7,13,-4,16,
grid(1),
graph(500,500,-7,13,-4,16,(3-3x)/(-1),15-3x),
circle(3,6,0.05),
circle(3,6,0.08),
circle(3,6,0.10)
)}}} 


Graph of {{{3x-y=3}}} (red) and {{{3x+y=15}}} (green) 




<hr>



B)


{{{2y-4x=3}}} Start with the second equation.



{{{-4x+2y=3}}} Rearrange the terms.





So we have the system of equations:

{{{system(2x-y=1,-4x+2y=3)}}}



{{{2(2x-y)=2(1)}}} Multiply the both sides of the first equation by 2.



{{{4x-2y=2}}} Distribute and multiply.



So we have the new system of equations:

{{{system(4x-2y=2,-4x+2y=3)}}}



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



{{{(4x-2y)+(-4x+2y)=(2)+(3)}}}



{{{(4x+-4x)+(-2y+2y)=2+3}}} Group like terms.



{{{0x+0y=5}}} Combine like terms.



{{{0=5}}}Simplify.



Since {{{0=5}}} is <font size="4"><b>never</b></font> true, this means that there are no solutions. 


So the system is inconsistent.