Question

8.$\

$$\begin{cases}3x + y = 11 \\\\ y = 2x + 1\\end{cases}$$

$point: (3, 7) yes / no9.$\

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

$point: (1, 1) yes / no10.$\

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

$point: (2, 3) yes / no11.$\

$$\begin{cases}y = 4 \\\\ x + y = 6\\end{cases}$$

$point: (2, 4) yes / no

Explanation:

Step1: Check (3,7) in Q8 eq1

Substitute $x=3, y=7$ into $3x+y=11$:
$3(3)+7=9+7=16
eq 11$

Step1: Check (1,1) in Q9 eq1

Substitute $x=1, y=1$ into $y=-x+2$:
$1=-1+2=1$

Step2: Check (1,1) in Q9 eq2

Substitute $x=1, y=1$ into $x+y=1$:
$1+1=2
eq 1$

Step1: Check (2,3) in Q10 eq1

Substitute $x=2, y=3$ into $2x-y=1$:
$2(2)-3=4-3=1$

Step2: Check (2,3) in Q10 eq2

Substitute $x=2, y=3$ into $y=x+1$:
$3=2+1=3$

Step1: Check (2,4) in Q11 eq1

Substitute $x=2, y=4$ into $y=4$:
$4=4$

Step2: Check (2,4) in Q11 eq2

Substitute $x=2, y=4$ into $x+y=6$:
$2+4=6$

Answer:

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