Answer:
The order for the systems is 2), 5),7), 1) and 3)
Step-by-step explanation:
To find the solution for ecah system first you have to choose a method, for example you can isolate one of the variables (x or y) in both equations and then equal each other.
1) 2x + y = 10 ⇒ y= 10 - 2x
x - 3y = -2 ⇒ -3y = -2 - x ⇒ y = (-2 - x)/-3 ⇒ y = 2/3 + (1/3)x
Now you have to equal both equations
10 - 2x = 2/3 + (1/3)x ⇒ 10 - 2/3 = (1/3)x + 2x ⇒28/3 = (7/3)x
⇒ (28/3)/(7/3) = x ⇒ 4.
With the "x" value obtained we return to the original equations and replace it there to find "y".
2x + y = 10 ⇒ 2(4) + y = 10 ⇒ y= 10 - 8 ⇒ y =2
The solution to the system is (4,2).
If you do the same for all the systems you will find that the solutions are
2) x + 2y = 5
2x + y = 4
Solution = (1, 2)
3) 5x + y = 33
x = 18 − 4y
Solution = (6,3 )
4) y = 13 − 2x
8x + 4y = 52
Solution = ∅, no solution
5) x + 3y = 5
6x − y = 11
Solution = (2, 1)
6) 2x + y = 10
-6x − 3y = -2
Solution = ∅, no solution.
7) y = 10 + x
2x + 3y = 45
Solution = (3, 13)
