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Hello out there,I really need some help with some problems,the first one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1

Hello out there,I really need some help with some problems,the first one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1.The next one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:x+y=4 and 2x-y=-7.The third one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=-x+2 and 3x+3y=6.And the last one is,Determine whether the system has one solution,no solution,or infinitely many solutions:y=2/3x and 2x-y=-4.Thanks to whoever can help.
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4x+2y=8 2x+y=1 --------- We will solve this by elimination since you don't say which to use; 1)4x+2y=8 2)2x+y=1 we will multiply a -2 to the second equation to eliminate the y; (-2)2x+y=1 -4x-2y=1 ------------- Now lets add the two equations together; 4x+2y=8 -4x-2y=-2 -------- 0=-2 Since this is o=-2, it is inconsistent ============================================== With this next one, when you add them together they already eliminate a variable, so no other multiplying is necessary; x+y=4 2x-y=-7 -------- 3x=-3 x=-1 Now substitute the -1 for x in one of the equations; -1+y=4 y=5 Since this has only one answer for x and y it is consistent and independent =============================================================================== y=-x+2 3x+3y=6 x+y=2 -3x-3y=-6 3x+3y=6 --------- 0=0 This is the same line so it is infinitely many solutions =============================================================== y=2/3x 2x-y=-4 ----------------- -2/3)x+y=0 2x-y=-4 ---------- {{{(4/3)x=-4}}} x=-3 {{{y=(2/3)(-3)}}} y=-2 This has only one point, so it has only one solution :)
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Hello out there,I really need some help with some problems,the first one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1
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