SOLUTION: Hello out there,I really need some help with some tough problems,the first one is Solve the system of linear equations by graphing:4x-y=6 and 3x+y=1.The next one is ,State whether

Question 104823: Hello out there,I really need some help with some tough problems,the first one is Solve the system of linear equations by graphing:4x-y=6 and 3x+y=1.The next one is ,State whether the system is consistent and independent,consistent and dependent,or inconsistent:4x+2y=8 and 2x+y=1.The third one is,State whether the system is consistent and independent,consistent and dependent,or inconsistent:x+y=4 and 2x-y=-7.And the last one is,Determine whether the system has one solution,no solution,or infinitely many solutions,y=-x+2 and 3x+3y=6.Thanks to whoever can help me.
Answer by cheesey(22) (Show Source): You can put this solution on YOUR website!
a) Graph each equation using the intercepts. Notice where the lines intersect, this point of intersection graphically represents a solution to the system.
b) if there is no solution, the system is inconsistent, if there are more than one solution the system is dependent, if there is only one unique solution, the system is independent. With the definitions in hand solve the system by solving one equation for one variable and plugging that into the other equation:
4x-y = 6 = > y = 4x - 6 , so 3x + y = 1 becomes 3x + (4x-6) = 1. Now solve this equation for x.
3x + 4x - 6 = 1 => 7 x = 7 => x = 1. Use this value of x to solve the first equation for y.
y = 4(1) - 6 = -2. One solution is (1, -2). At this point you may graph the system to see if there are more solutions. Try solving the second equation for y first.
c) use the same steps as in b)
d) use the same steps as in b)
Tip: It is easier to tell graphically if the system is consisent or inconsistent. If the lines are parallel then no solution exists. If the lines intersect at only one point - independent. However, if the lines intersect at every point, then the system is dependent
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