I need help with systems of linear equations solved through elimination.

Question

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

Answer 1

1) Rewrite a little

8x-3y = 38

9x+6y = 24

Add 2 times the first equation to the second

16x-6y = 76

9x+6y = 24

----------------------

25x = 100 -->x = 100/25 = 4

Substitute 4 for x into the first equation

8(4) -3y = 38 --> -3y = 6 --> y = -2

(4, -2)

2)

2x+y = 6

7x+3y = 3

Subtract 3 time the first equation from the second

7x+3y=3

-6x-y=-18

------------

x = -15

2(-15)+y = 6 -->y = 36

(-15,36)

3)

11x -10y = 5

2x + 7y = 45

Add 10/7 times the second equation to the first

11x -10y = 5

(20/7)x +10y = 45(10/7)

---------------------------

(97/7)x = 35/7 +450/7 = 485/7

x = (485/7)(7/97) = 5

55 - 10 y = 5 --> y = 50/10 --> y = 5

(5,5)