Slope: 3

Y-intercept : (0,9)

**Answer:**

see the explanation

**Step-by-step explanation:**

we know that

we have

so

Remember that

substitute

----> is verified

**Answer:**

No

**Step-by-step explanation:**

5x-2y=24

5x=24+2y____equ 1

2x+y=6

Y=6-2x______equ 2

Now substitute the value of y in equation 1

5x=24+2y

5x=24+2(6-2x)

5x=24+12-4x

5x+4x=36

X=36/9

X=4

Now, put the value of x in equation 2

Y=6-2x

Y=6-2*4

Y= -2

(4,-2)

**Answer:**

78 persons

**Step-by-step explanation:**

**Given**

**Required**

Determine the maximum number of person that can be invited

**Let the number of persons be p.**

**If the hall charges $37 for 1 person, then it will charge $37p for p persons.**

**So:**

**The expression becomes:**

**Substitute values for Clean up, Charges and Budget**

**Subtract 100 from both sides**

**Make p the subject**

**Round down**

<em>**Hence, they can only invite 78 people to stay within budget**</em>

**Answer:**

EG is **19 units**

**Step-by-step explanation:**

Let us solve the question

∵ Lines CD and EF intersected at point G

∴ **CD = CG + GD**

∴ **EF = EG + GF**

∵ Line EF **bisects** line CD

→ That means G is the midpoint of CD

∴ **CG = GD**

∵ CG = 5x -1

∵ GD = 7x - 13

→ Equate them to find x

∴ **7x - 13 = 5x -1**

→ Add 13 to both sides

∴ 7x -13 + 13 = 5x - 1 + 13

∴ 7x = 5x + 12

→ Subtract 5x from both sides

∴ 7x - 5x = 5x - 5x + 12

∴ 2x = 12

→ Divide both sides by 2

∴

∴ **x = 6**

∵ EF = 6x - 4

→ Substitute x by 6 to find its length

∴ EF = 6(6) - 4 = 36 - 4

∴ **EF = 32**

∵ EF = EG + GF

∵ GF = 13

∴ 32 = EG + 13

→ Subtract 13 from both sides

∵ 32 - 13 = EG + 13 - 13

∴ 19 = EG

∴ **EG = 19 units**