Mathematics College

I need help with solving systems of linear equations through elimination.
1.) 8x = 3y + 38
24= 6y + 9x
a. all real numbers
b. (4,-2)
c. (4,-4)
d. (6,3)
2.) 6 = 2x + y
7x = 3 - 3y
a. (15,-36)
b. (-5,6)
c. (0,0)
d. (-15,36)
3.) 11x = 5 + 10y
7y = -2x +45
a. (-5,10)
b. (5,5)
c. (14, -4)
d. No solution

Answers

Answer 1

Answer:

See explanation

Step-by-step explanation:

8x = 3y + 38  

24= 6y + 9x  

Rearrange;

3y - 8x = -38       * 2     -------(1)

6y + 9x = 24       * 1       -------(2)

6y - 16x = -76    -------(3)

6y + 9y  = 24    -------(4)

Subtract (4) from (3)

     -25y = -100

      y= 100/25

     y = 4

Substitute y =4 into(1)

3y - 8x = -38    

3(4) - 8x = -38

12 -8x = -38

-8x = -38 - 12

x = 50/8 = 6 2/8

2) 6 = 2x + y

7x = 3 - 3y

Rearrange;

2x + y = 6            * 3    --------(1)

7x + 3y = -3         * 1     --------(2)

6x + 3y = 18        ---------(3)

7x  + 3y = -3        ---------(4)

Subtract (4) from (3)

-x   = 21

x = -21

Substitute x = -21 into (1)

2x + y = 6

2(-21) + y = 6

-42 + y = 6

y = 6 + 42

y = 48

3)  

11x = 5 + 10y

7y = -2x +45

Rearrange

11x - 10y = 5          * 2  ---------(1)

2x + 7y   = 45       * 11  ---------(2)

22x - 20y = 10     --------(3)

22x + 77y = 495  --------(4)

Subtract (4) from (3)

       -97y  = -485

          y =  5

Substitute y =5 into (1)

11x - 10y = 5  

11x - 10(5) = 5

11x - 50 = 5

11x = 5 + 50

11x = 55

x = 55/11

x = 5

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