Question

Determine whether the point (1,8) is a solution to the equations given in the first column and tick the correct option.

Equations
Yes
No
x+y=9
2x+2y≤18
3x+y>12
x+2y>17

Answer 1

Part 1)
`x+y=9` ----> Yes

Part 2)
`2x+2y\leq 18` ----> Yes

Part 3)
`3x+y>12` ----> No

Part 4)
`x+2y>17` ----> No

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

`x+y=9`

For x=1, y=8

`1+8=9`

`9=9` ---> is true

so

Yes, the point is a solution

case 2) we have

`2x+2y\leq 18`

For x=1, y=8

`2(1)+2(8)\leq 18`

`18\leq 18` -----> is true

so

Yes, the point is a solution

case 3) we have

`3x+y>12`

For x=1, y=8

`3(1)+8>12`

`11>12` -----> is not true

so

No, the point is not a solution

case 4) we have

`x+2y>17`

For x=1, y=8

`1+2(8)>17`

`17>17` -----> is not true

so

No, the point is not a solution