Question

The equations 4x+10y=4 and -8x+6y= -60 are Select one:
Consistent
Inconsistent
Consistent with unique solution
Data not sufficient​

Answer 1

Answer:

C

Step-by-step explanation:

Consistent with unique solution

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Answer 2

Consistent with unique solution

Explanation:

Given equations:

4x + 10y = 4

-8x + 6y = -60

a1 = 4, b1 = 10, c1 = 4

a2 = -8, b2 = 6, c2 = -60

$\sf{\longrightarrow\:\dfrac{a_1}{a_2}=\dfrac{4}{-8}=-\dfrac{1}{2}}$

$\sf{\longrightarrow\:\dfrac{b_1}{b_2}=\dfrac{10}{6}=\dfrac{5}{3}}$

$\sf{\longrightarrow\:\dfrac{c_1}{c_2}=\dfrac{-60}{4}=-15}$

Here, we can clearly see that:

$\sf{\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}}$

meaning that the given system has a consistent and unique solution.

Therefore, the required correct answer is Option C: Consistent with unique solution.

Knowledge Bytes:

All two linear equation in two variables have solutions that are either consistent or inconsistent. This is found out by comparing the coefficients of the two equations.

For the equations a1x + b1y + c1 = 0 and a2x + a2y + c2 = 0, the three possibilities are:

$\sf{\longrightarrow\:\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}}$

- Such a system will have a consistent and a single, unique solution. In the graph of such a system, the lines would be intersecting at a particular point.

$\sf{\longrightarrow\:\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}}$

- Such a system will have consistent and infinite number of solutions. In the graph of such a system, the lines would be overlapping each other.

$\sf{\longrightarrow\:\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}}$

- Such a system will have no solution and is inconsistent. In the graph of such a system, the lines would be parallel to each other.