Question

Select the pair of linear equations that are consistent .

2−3 = 7     ;     4−6 = 112x−3y = 7     ;     4x−6y = 11

−2 = 0     ;    3+6 = 8   x−2y = 0     ;    3x+6y = 8   

3 +5 =12  ;   6+10 =6 3x +5y =12  ;   6x+10y =6 

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Answer 1

Answer:

6x+10y=6

Step-by-step explanation:

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Answer 2

Answer:

(2). x - 2y = 0 and 3x + 6y = 8

Step-by-step explanation:

The system of linear equations is consistent, if it has at least one solution.

If a consistent system has exactly one solution, it is independent consistent system of linear equations. If a consistent system has an infinite number of solutions, it is dependent.

$a_{1}x + b_{1}y = c_{1}$

$a_{2}x + b_{2}y = c_{2}$

If $\frac{a_{1}}{a_{2}}$ ≠ $\frac{b_{1}}{b_{2}}$ system has unique solution

If  $\frac{a_{1}}{a_{2}}$ = $\frac{b_{1}}{b_{2}}$ = $\frac{c_{1}}{c_{2}}$ system has infinitely many solutions

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2x - 3y = 7

4x - 6y = 11

$\frac{2}{4}$ = $\frac{-3}{-6}$ ≠ $\frac{7}{11}$ ⇒ system has no solutions and inconsistent.

x - 2y = 0

3x + 6y = 8

$\frac{1}{3}$ ≠ $\frac{-2}{6}$ ≠ $\frac{0}{8}$ ⇒ system has exactly one solution, it is independent consistent

3x + 5y = 12

6x + 10y = 6

$\frac{3}{6}$ = $\frac{5}{10}$ ≠ $\frac{12}{6}$ ⇒ system has no solutions and inconsistent.