Part 1) option D) No solutions
Part 2) option C ![y=9](/tpl/images/0355/2790/8bf3d.png)
Part 3) option E ![E(0,-3)](/tpl/images/0355/2790/e88c4.png)
Step-by-step explanation:
Part 1) we have
-------> equation A
-------> equation B
Divide the equation B by
both sides
--------> ![3x-2y=7](/tpl/images/0355/2790/92738.png)
Equation A and equation B represent a parallel lines, because their have the same slope ![m=\frac{3}{2}](/tpl/images/0355/2790/b72be.png)
therefore
The system of equation does not have solution
Part 2) we have
-------> equation A
-------> equation B
Multiply the equation A by
both sides
------->
-------> equation C
Multiply the equation B by
both sides
------>
------> equation D
Adds equation C and equation D
![20x+16y=4\\-20x-15y=5\\---------\\16y-15y=4+5\\ y=9](/tpl/images/0355/2790/b37f7.png)
Part 3) we have
-------> inequality A
-------> inequality B
we know that
If a point lie in the solution set of the system of inequalities, then the point must be satisfy the inequalities of the system
a) point ![C(1,0)](/tpl/images/0355/2790/effcd.png)
Verify inequality A
![0](/tpl/images/0355/2790/757ed.png)
-------> is true
Verify inequality B
![0](/tpl/images/0355/2790/aac92.png)
-----> is not true
therefore
the point
does not lie in the solution set of the system of inequalities
b) point ![D(-5,-2)](/tpl/images/0355/2790/53cc5.png)
Verify inequality A
![-2](/tpl/images/0355/2790/df9d3.png)
-------> is not true
therefore
the point
does not lie in the solution set of the system of inequalities
c) point ![E(0,-3)](/tpl/images/0355/2790/e88c4.png)
Verify inequality A
![-3](/tpl/images/0355/2790/aaf22.png)
-------> is true
Verify inequality B
![-3](/tpl/images/0355/2790/50378.png)
-----> is true
therefore
the point
lies in the solution set of the system of inequalities
d) point ![F(-1,5)](/tpl/images/0355/2790/60d65.png)
Verify inequality A
![5](/tpl/images/0355/2790/0cd95.png)
-------> is not true
therefore
the point
does not lie in the solution set of the system of inequalities