Answer/Step-by-step Explanation:

1. 3x + y = 11 => equation 1

5x - y = 21 => equation 2

Subtract equation 2 from equation 1 to eliminate y variable

3x + y = 11

5x - y = 21

-2x = - 10

Divide both sides by -2

-2x/-2 = -10/-2

x = 5

Substitute x = 5 into equation 1 or 2:

3x + y = 11 => equation 1

3(5) + y = 11

15 + y = 11

y = 11 - 15 (subtraction 15 from each side)

y = -4

Solution: x = 5, y = -4

2. 5x + 12y = -34 => equation 1

2x + 4y = -12 => equation 2

Multiply equation 1 by 2, multiply equation 2 by 5.

2(5x + 12y = -34) => 10x + 24y = -68 => eqn 3

5(2x + 4y = -12) => 10x + 20y = -60 => eqn 4

Subtract eqn 4 from eqn 3

4y = -8

Divide both sides by 4

y = -2

Substitute y = -2 into equation 2

2x + 4y = -12 => equation 2

2x + 4(-2) = -12

2x - 8 = -12

2x = -12 + 8 (adding 8 to both sides)

2x = -4

Divide both sides by 2

x = -2

Solution: x = -2, y = -2