Question

determine whether pair of linear equations is consistent or inconsistent.x+2y=4,3x+6y=12
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Answer 1

Answer

X+2y=4,3x+6y=12

a¹=1,b¹=2,c¹=4

a²=3,b²=6,c²=12

a¹/a²=1/3

b¹/b²=2/6=1/3

c¹/c²=-4/-12=1/3

a¹/a²=b¹/b²=c¹/c²

The following pair of linear equations are consistent

Answer 2

Answer: Equation is consistent.

Step-by-step explanation:

Given : x + 2y = 4

            3x + 6y = 12

To find : Whether the pair of linear equation is consistent or not.

Solution :

For the pair of linear equation to be consistent, either it should have distinct solution or infinite solution.

$a_{1} = 1, b_{1} = 2, c_{1} = 4$

$a_{2} = 3, b_{2} = 6, c_{2} = 12$

∴ $\frac{a_{1} }{a_{2} } = \frac{1}{3}$

∴ $\frac{b_{1} }{b_{2} } = \frac{2}{6} = \frac{1}{3}$

∴ $\frac{c_{1} }{c_{2} } = \frac{4}{12} = \frac{1}{3}$

∴ The solution is consistent and have infinite solutions.

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