Question

Which system of equations is consistent and dependent?
{3x+2y=3
6x+4y=6
{4x+ 6y= 2
4x+6y=1
{2x+3y=-6. 2x+3y=-12
{5x+4y=-30
3x-9y=-18

Answer 1

Answer:

A.

Step-by-step explanation:

Took it on Edge2020 :)

Answer 2

$3x+2y=3$, $6x+4y=6$ system of equations is consistent and dependent.

Option A is correct

What is meant by system of equations?

System of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

If $\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} }=\frac{c_{1} }{c_{2} }$ then the lines coincides and the pair of equations is dependent and consistent.

If $\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} }\neq\frac{c_{1} }{c_{2} }$ then the pair of linear equations in two variables is said to be inconsistent.

If $\frac{a_{1} }{a_{2} } \neq\frac{b_{1} }{b_{2} }$ then the pair of linear equations in two variables is said to be consistent.

System 1 :

$3x+2y=3$-----------1

$6x+4y=6$ ---------- 2

$\frac{3}{6} =\frac{2}{4} =\frac{3}{6}$

⇒ $\frac{1}{2} =\frac{1}{2} =\frac{1}{2}$

If $\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} }=\frac{c_{1} }{c_{2} }$ then the lines coincides and the pair of equations is dependent and consistent.

The system of equations is dependent and consistent

System 2 :

$4x+ 6y= 2\\\\4x+6y=1$

$\frac{4}{4} =\frac{6}{6} =\frac{2}{1}$

⇒ 1 = 1 ≠ 2

If $\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} }\neq\frac{c_{1} }{c_{2} }$ then the pair of linear equations in two variables is said to be inconsistent.

The system of equations is inconsistent.

System 3 :

$2x+3y=-6\\\\2x+3y=-12$

$\frac{2}{2} =\frac{3}{3} =\frac{-6}{-12}$

1 = 1 ≠ -2

If $\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} }\neq\frac{c_{1} }{c_{2} }$ then the pair of linear equations in two variables is said to be inconsistent.

The system of equations is inconsistent.

System 4 :

$5x+4y=-30\\\\3x-9y=-18$

$\frac{5}{3} =\frac{4}{-9} =\frac{-30}{-18}$

If $\frac{a_{1} }{a_{2} } \neq\frac{b_{1} }{b_{2} }$ then the pair of linear equations in two variables is said to be consistent.

The system of equations is consistent.

Hence, $3x+2y=3$, $6x+4y=6$ system of equations is consistent and dependent.

Option A is correct.

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