# Assorted Linear System of Equation Questions

Solve linear system of equation

x - 3y = -6

5x + 3y = 42

#### Solution Preview

1. add equation 1 with equation 2 to get 6x=36, hence x=6. substitute x=6 into equation 1 to get y=4. choose A

2. add equation 1 with 3 times of equation 2 to get 17x=37, hence x=37/17. substitute x=37/17 into equation 1 to get y=-15/34. choose B

3. minus equation 1 with 4 times of equation 2 to get 0=-23 which is impossible. choose d: no solution

4. minus 3 times of equation 1 with equation 2 to get 0=7 which is impossible. choose d: no solution

5. add equation 1 with 3 times of equation 2 to get 10x=30, hence x=3. substitute x=3 into equation 1 to get y=2. choose A

6. minus 2 times of equation 1 with equation 2 to get 0=0 which is correct all the times. so the system has infinitely many solution. let y=k, so x=5k/2+5. choose D

7. minus equation 1 with 7 times of equation 2 to get -27y=-54, hence y=2. substitute y=2 into equation 1 to get x=4. choose B

8. minus 5 times of equation 1 with equation 2 to get 0=197 which is impossible. choose d: no solution

9. ture. if two line are not parallel. they will intersect at least one time. such intersections are the solutions.

10. minus equation 1 with 2 times of equation 2 to get -27y=34. hence y=-2. ...

#### Solution Summary

The solution gived detailed steps on solving various questions on the linear system of equations. All formula and calcuations are shown and explained.