linear systems?

Question

okay i'm doing linear systems and it says to decide whether the ordered pair is a solution of the linear system. (1,5) and the system is
3x - y = -2
-4x + 2y= 5

how would you do that?
and how do you state whether a linear system has one solution, many solutions, or no solution when there is a graph?

Answer 1

Let x=1 and y=5. Plug those into the equations. If the statements remain true after simplifying, then the ordered pair is a solution. If not, and you get something like "1=2" when you simplify, then you know the ordered pair isn't a solution.

When you're looking at lines like this on a two-dimensional graph, remember any point on a given line is a solution for that particular equation. So if there are points in common with the lines, then those points represent ordered pairs of solutions.

Two lines can either cross at some point (showing that there's one solution), completely overlap each other (showing infinately many solutions), or be parallel (showing no solutions).

Answer 2

Substitute x = 1 and y = 5 and see if the equations work:
3(1) - 5 = -2, true
-4(1) + 2(5) = 5, false. So it's not a solution.

If there's a graph, presumably with two lines on it, if the lines are the same (on top of each other) there are infinitely many solutions; if they intersect at a single point there is one solution; if they are parallel but distinct there are no solutions.

Answer 3

for a given point to be a solution of a system it has to satisfy both equations:

3(1) - 5 = -2 true
-4(1) +2(5) = 6 and not 5
so, not a solution

one solution: two lines intersect
many solution: two equations are the same line
no solution: have two parallel lines

Answer 4

Fill in the numbers (not sure, its been a while)

3(1)-(5) = -2
-2 = -2 true

-4(1) + 2(5) = 5
-4 + 10 = 5
6 = 5 false

Answer 5

there is unique solution and the solution is
x=1/2 y=7/2

Answer 6

just plug in da number (1,5) 1 is da x axis and 5 iz da y axis

if u answer a linear sys.... den if da answer iz (0,0) den its infintly many solution

one solution mean its (0,?) qustion mark is another number

no solution would be sumthin like diz.... (5,13)

Answer 7

if the rank of the equations is the same of the number of variables, there is one solution. if less, many solutions. otherwise, no solutions.