Question

Solve these systems of equations Using the elimination method.

a). 3x + y = 13 b) 6x - y = 14
x - 5y = 15 2x + y = 12





c) 3x - 4y = 22
2x + 5y = 7

Answer 1

a). 3x + y = 13
x - 5y = 15
multiplier equation 1 by 5
15x+5y=65
DSA
15x+5y=65
x - 5y = 15
remaining
16x=80
x=5
5-5y=15
-5y=15-5
-5y=10
y=10 ÷ -5
y=-2
x,y
5,-2

Answer 2

a. 3x + y = 13 → 15x + 5y = 65
x - 5y = 15 → x - 5y = 15
16x = 80
16 16
x = 5
x - 5y = 15
5 - 5y = 15
- 5 - 5
-5y = 10
-5 -5
y = -2
(x, y) = (5, -2)

b. 6x - y = 14
2x + y = 12
8x = 26
8 8
x = 3¹/₄
6x - y = 14
6(3¹/₄) - y = 14
19¹/₂ - y = 14
- 19¹/₂ - 19¹/₂
-y = -5¹/₂
-1 -1
y = 5¹/₂
(x, y) = (3¹/₄, 5¹/₂)

c. 3x - 4y = 22 → 15x - 20y = 110
2x + 5y = 7 → 8x + 20y = 28
23x = 138
23 23
x = 6
3x - 4y = 22
3(6) - 4y = 22
18 - 4y = 22
- 18 - 18
-4y = 4
-4 -4
y = -1
(x, y) = (6, -1)