Question

Which of the following is the correct classification of the system of equations below?Which of the following is the correct classification of the system of equations below?
A. parallel



B. coincident



C. intersecting

Answer 1

Answer: Hence, Option 'c' is correct.

Step-by-step explanation:

Since we have given that

$-x+2y=10\\\\6y=-12x+1\\\\\implies 12x+6y=1$

First we find the ratio of coefficients per variable and constant:

$\dfrac{a_1}{a_2}=\dfrac{-1}{12}$

and

$\dfrac{b_1}{b_2}=\dfrac{2}{6}=\dfrac{1}{3}$

and

$\dfrac{c_1}{c_2}=\dfrac{10}{1}$

Since we can see that all three are not equal to each other i.e.

$\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$

so,it is considered as intersecting lines.

Hence, Option 'c' is correct.

Answer 2

-x + 2y = 10
6y = -12x + 1

6y = -12x + 1
 6           6
  y = -2x + ¹/₆

                 -x + 2y = 10
    -x + 2(-2x + ¹/₆) = 10
-x + 2(-2x) + 2(¹/₆) = 10
           -x - 4x + ¹/₃ = 10
                -5x + ¹/₃ = 10
                       - ¹/₃   - ¹/₃
                       -5x = 9²/₃
                        -5     -5
                          x = -1¹⁴/₁₅

y = -2x + ¹/₆
y = -2(-1¹⁴/₁₅) + ¹/₆
y = 3¹³/₁₅ + ¹/₆
y = 4¹/₃₀
(x, y) = (-1¹⁴/₁₅, 4¹/₃₀)

It is intersecting, making the answer equal to C.