i have an exam tomorrow i want the answer so i can check if my answers are right

Question

Determine whether the lines for the pair of equations are parallel, perpendicular, or neither.

4x + 3y = -30

6x - 8y = 20

A gym charges a fee to join plus a monthly fee. Joining plus 3 months costs $155. Joining plus 6 months costs $215. Write a system of equations that describes the given situation. Use j for the joining fee and m for the number of months.

The sum of two numbers is 78. Their difference is 34. Write a system of equations that describes the situation. Then, solve the system.

Solve the system.

3x + 2y = 7

y = -3x + 11

Solve the system.

6x + 3y = -12

6x + 2y = -4

Sam is older than Mike. The sum of their ages is 25. The difference between their ages is 3. How old is Mike?

Solve the system.

3x - 4y = -24

x + y = -1

Answer 1

4x+3y =-30, slope = -4/3

6x -8y =20 slope = 6/8 = 3/4

slopes are negative inverses, so the lines are perpendicular

C= 155 = j +3M

C =215 = j +6M

subtract 1st from 2nd to get 60=3M, monthly charge = $20

j=155-3(20) = 155-60 = $95 = joining fee

x+y= 78

x-y=34

2x = 112

x =112/2 = 56

y = 78-56 = 22

numbers are 22 and 56

3x +2y = 7

y= -3x +11

3x +2(-3x+11) = 7

3x -6x +22 = 7

22-7 = 3x

3x = 15

x = 15/3 = 5

y = -3(5)+11 =-15+11 =- 4

x=5, y=-4

6x+3y =-12

-6x +2y =-4 add them to get

5y =-16

y =-16/5

6x =-12-3(-16/5)= -12 +48/5 = -12/5

x = -2/5

x=-2/5 =-0.4, y=-16/5 =-3.2

S+M = 25

S-M =3

2S =28

S=14 years old for Sam's age

M=25-14 = 11 years old for Mike

3x-4y =-24

x+y = -1

3x+3y=-3

subtract last from 1st to get

-7y =-21

y = 3

x =-1-3 =-4

x=-4