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
