Question

Which equation can pair with x + 2y = 5 to create an inconsistent system?

Answer 1

Answer:

only (1) and (3)  forms a pair of inconsistent system with x + 2y = 5.

Step-by-step explanation:

Given : a linear equation   x + 2y = 5

We have to find a pair of equation that can pair with x + 2y = 5 to create an inconsistent system.

Consider a system of equation $a_1x+b_1y+c_1=0 \\\\a_2x+b_2y+c_2=0$

For the system to have no solution the condition is,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$

We just have to check for the above condition, those pair whose x and y coefficient are in same ratio and constant coefficient are different, those pair will form an inconsistent system.

Thus, only (1) and (3) are multiple of given equation, thus forms a pair of inconsistent system.

Answer 2

X + 2y = 5
x = 5 - 2y

2x + 4y = 3
2(5-2y) + 4y = 3
10 - 4y + 4y = 3
10 ≠ 3

5x + 2y = 3
5(5-2y) + 2y = 3
25 - 10y + 2y = 3
-8y = 3 - 25
-8y = -22
y = -22/-8
y = 2.75

6x + 12y = 30
6(5-2y) + 12y = 30
30 -12y + 12y = 30
30 = 30

3x + 4y = 8
3(5-2y) + 4y = 8
15 - 6y + 4y = 8
-2y = 8 - 15
-2y = -7
y = -7/-2
y = 3.5

An inconsistent system is a system of equation that has NO SOLUTIONS.

2x + 4y = 3 is the equation to be paired with x + 2y = 50 to create an inconsistent system.