LINEAR ALGEBRA I am trying to review for my up coming test a

LINEAR ALGEBRA: I am trying to review for my up coming test and I am having a problem determining which of the points (1,-2,-1,3),(-1,0,2,1), and (-2,-1,4,-3) satisfy the liear system

3x₁ - x₂ + 2x₃ =1 and 2x₁+3x₂-1x₄=-3

is there a way i can graph this to determine the answer? how would i plug it in?

Solution

(1,-2,-1,3),(-1,0,2,1), and (-2,-1,4,-3) satisfy the liear system

3x1 - x2 + 2x3 =1 and 2x1+3x2-1x4=-3

(1 , -2 , -1 ,3) :
Check first equation.....
3x1 - x2 + 2x3 =1
3(1) - (-2) + 2(-1) = 1
3 + 2 - 2 = 1
3 = 1
FALSE

So, not the first point

(-1,0,2,1) :
Check first equation.....
3x1 - x2 + 2x3 =1
3(-1) - 0 + 2(2) = 1
-3 + 4 = 1
1 = 1
TRUE

Check second equation as well
2x1+3x2-1x4=-3
2(-1) + 3(0) - 1 = -3
-2 - 1 = -3
-3 = -3
TRUE

So, since both equations satisfy, the point is (-1,0,2,1)