x + 5x = -2
6x = -2
6 6
x = ⁻¹/₃
x + 5y = 4
⁻¹/₃ + 5y = 4
+ ¹/₃ + ¹/₃
5y = 4¹/₃
5 5
y = ¹³/₁₅
(x, y) = (⁻¹/₃, ¹³/₁₅)
It is consistent and independent.
y = 3x + 4
-2x + y = 4
-2x + y = 4
-2x + 3x + 4 = 4
x + 4 = 4
- 4 - 4
x = 0
y = 3x + 4
y = 3(0) + 4
y = 0 + 4
y = 4
(x, y) = (0, 4)
It is consistent and independent.
y = -x + 3
2x + 2y = 6
2x + 2y = 6
2x + 2(-x + 3) = 6
2x + 2(-x) + 2(3) = 6
2x - 2x + 6 = 6
6 = 6
It is consistent and dependent.
5x + 2y = -4
5x - 2y = 3
10x = -1
10 10
x = ⁻¹/₁₀
5x + 2y = -4
5(⁻¹/₁₀) + 2y = -4
⁻¹/₂ + 2y = -4
+ ¹/₂ + ¹/₂
2y = -3¹/₂
2 2
y = -1³/₄
(x, y) = (⁻¹/₁₀, -1³/₄)
It is consistent and independent.
