Answer:
Part 1) [tex]x+y=9[/tex] ----> Yes
Part 2) [tex]2x+2y\leq 18[/tex] ----> Yes
Part 3) [tex]3x+y>12[/tex] ----> No
Part 4) [tex]x+2y>17[/tex] ----> No
Step-by-step explanation:
we know that
If a point is a solution of a equation, then the point must satisfy the equation (makes true the equation)
we have the point (1,8)
Verify each case
Substitute the value of x and the value of y in each equation
case 1) we have
[tex]x+y=9[/tex]
For x=1, y=8
[tex]1+8=9[/tex]
[tex]9=9[/tex] ---> is true
so
Yes, the point is a solution
case 2) we have
[tex]2x+2y\leq 18[/tex]
For x=1, y=8
[tex]2(1)+2(8)\leq 18[/tex]
[tex]18\leq 18[/tex] -----> is true
so
Yes, the point is a solution
case 3) we have
[tex]3x+y>12[/tex]
For x=1, y=8
[tex]3(1)+8>12[/tex]
[tex]11>12[/tex] -----> is not true
so
No, the point is not a solution
case 4) we have
[tex]x+2y>17[/tex]
For x=1, y=8
[tex]1+2(8)>17[/tex]
[tex]17>17[/tex] -----> is not true
so
No, the point is not a solution
