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Solving Simultaneous Linear Equations by Cross Multiplication Method

2x – 4y = 7 x...

Question

2x – 4y = 7
x – 3y = –2
The given set of equations has______.

Unique solution

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Many solutions

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None of these

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No solution

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Solution

The correct option is A Unique solution
For the given set of equations,
$\frac{2}{1} \neq \frac{4}{3}$
$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
It has a unique solution and the set of equations are consistent
Hence, option a is the correct answer.

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Similar questions

2 x + 3 y = 5, x - y = 2, x + 4 y = a

2 x + 3 y = 7; (a + b + 1) x + (a + 2 b + 2) y = 4 (a + b) + 1

Find the values of a and b for which the following system of equations has infinitely many solutions:

(i) (2a - 1) x - 3y = 5

3x + (b - 2) y = 3

(ii) 2x - (2a + 5) y = 5

(2b + 1) x - 9y = 15

(iii) (a - 1) x + 3y = 2

6x + (1 - 2b) y = 6

(iv) 3x + 4y = 12

(a + b) x + 2 (a - b) y = 5a - 1

(v) 2x + 3y = 7

(a - b) x + (a + b) y = 3a + b - 2

(vi) 2x + 3y - 7 = 0

(a - 1) x + (a + 1) y = (3a - 1)

(vii) 2x + 3y = 7

(a - 1) x + (a + 2) y = 3a

(viii) x + 2y = 1

(a - b) x + (a + b) y = a + b - 2

(ix) 2x + 3y = 7

2ax + ay = 28 - by

a

2 x + 3 y = 5, x - y = 2, x + 4 y = a

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