Question

12.$\

$$\begin{cases} y=3x \\\\ 2x + y = 9 \\end{cases}$$

$point: (3,9) yes / no13.$\

$$\begin{cases} x - y = 1 \\\\ y = 2 \\end{cases}$$

$point: (3,2) yes / no14.$\

$$\begin{cases} y = -2x + 8 \\\\ x + y = 5 \\end{cases}$$

$point: (1,6) yes / no15.$\

$$\begin{cases} 3x + 2y = 12 \\\\ y = 3 \\end{cases}$$

$point: (2,3) yes / no

Explanation:

Step1: Check (3,9) in system 12

Substitute $x=3, y=9$ into $y=3x$: $9=3(3) \implies 9=9$ (true). Substitute into $2x+y=9$: $2(3)+9=6+9=15
eq9$ (false).

Step2: Check (3,2) in system 13

Substitute $x=3, y=2$ into $x-y=1$: $3-2=1$ (true). Substitute into $y=2$: $2=2$ (true).

Step3: Check (1,6) in system 14

Substitute $x=1, y=6$ into $y=-2x+8$: $6=-2(1)+8 \implies 6=6$ (true). Substitute into $x+y=5$: $1+6=7
eq5$ (false).

Step4: Check (2,3) in system 15

Substitute $x=2, y=3$ into $3x+2y=12$: $3(2)+2(3)=6+6=12$ (true). Substitute into $y=3$: $3=3$ (true).

Answer:

1. NO
2. YES
3. NO
4. YES