Question 207645
I'll do the first two to get you going in the right direction.



# 1


{{{x-3y=7}}} Start with the first equation.



{{{x=3y+7}}} Add 3y to both sides.



{{{-3x+16y=28}}} Move onto the second equation



{{{-3(3y+7)+16y=28}}} Plug in {{{x=3y+7}}} 



{{{-9y-21+16y=28}}} Distribute.



{{{7y-21=28}}} Combine like terms on the left side.



{{{7y=28+21}}} Add {{{21}}} to both sides.



{{{7y=49}}} Combine like terms on the right side.



{{{y=(49)/(7)}}} Divide both sides by {{{7}}} to isolate {{{y}}}.



{{{y=7}}} Reduce.



{{{x=3y+7}}} Go back to the first isolated equation.



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



{{{x=21+7}}} Multiply.



{{{x=28}}} Combine like terms.



So the solutions are {{{x=28}}} and {{{y=7}}} which form the ordered pair (28,7)



This means that the system is consistent and independent.


<hr>



# 2


{{{-2x+y=0}}} Start with the first equation.



{{{y=2x}}} Add {{{2x}}} to both sides.



{{{3x+7y=17}}} Move onto the second equation.



{{{3x+7(2x)=17}}} Plug in {{{y=2x}}}.



{{{3x+14x=17}}} Multiply.



{{{17x=17}}} Combine like terms on the left side.



{{{x=(17)/(17)}}} Divide both sides by {{{17}}} to isolate {{{x}}}.



{{{x=1}}} Reduce.



-------------------------------------------



Since we know that {{{x=1}}}, we can use this to find {{{y}}}.



{{{y-2x=0}}} Go back to the first equation.



{{{y-2(1)=0}}} Plug in {{{x=1}}}.



{{{y-2=0}}} Multiply.



{{{y=0+2}}} Add {{{2}}} to both sides.



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



So the solutions are {{{x=1}}} and {{{y=2}}} which form the ordered pair (1,2)



This means that the system is consistent and independent.



Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(1,2\right)]. So this visually verifies our answer.



{{{drawing(500,500,-9,11,-8,12,
grid(1),
graph(500,500,-9,11,-8,12,0+2x,(17-3x)/(7)),
circle(1,2,0.05),
circle(1,2,0.08),
circle(1,2,0.10)
)}}} Graph of {{{y-2x=0}}} (red) and {{{3x+7y=17}}} (green)