Question

What are the classifications of each system?

Answer 1

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 inconsistent 
y = 3x + 4-2x + y = 4
        -2x + y = 4-2x + 3x + 4 = 4           x + 4 = 4               - 4  - 4                 x = 0y = 3x + 4y = 3(0) + 4y = 0 + 4y = 4(x, y) = (0, 4)It is consistent and independent.
y = -x + 32x + 2y = 6
             2x + 2y = 6    2x + 2(-x + 3) = 62x + 2(-x) + 2(3) = 6         2x - 2x + 6 = 6                        6 = 6It is consisteent
5x + 2y = -4 5x - 2y = 3      10x = -1       10    10           x = ⁻¹/₁₀
     5x + 2y = -45(⁻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.

sorry if i used your thing but i took the quiz and this is right im sorry but that's wrong :(

Answer 2

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.