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Simultaneous Linear Equations

Check whether...

Question

Check whether system of simultaneous equations $2 x + y = 4$ and $y = 2 x$ have unique solution or not?

A

Yes it has unique solution

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B

No, it does not have unique solution

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Solution

The correct option is A Yes it has unique solution
On plotting the given simultaneous equations on cartesian plane, we get:

Clearly, both the lines are intersecting at a single point.
So, this system has only one solution or unique solution.

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Similar questions

Q. Without actually solving the simultaneous equations given below, decide which simultaneous equations have unique solutions, no solution or infinitely many solutions.

(vi) \frac{x}{2} + \frac{y}{3} = 4; \frac{x}{4} + \frac{y}{6} = 2

Q. Without actually solving the simultaneous equations given below,
decide which simultaneous equations have unique solutions ,
no solution or infinitely many solutions.

(i) 3 x + 5 y = 16; 4 x - y = 6

Without actually solving the simultaneous equations given below, decide whether the system has unique solution, no solution or infinitely many solutions.

\frac{x}{2} + \frac{y}{3} = 4; \frac{x}{4} + \frac{y}{6} = 2

Q. In the following given systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it

2 x + y = 5

4 x + 2 y = 10

Determine whether the following system of linear equations have no solution, infinitely many solution or unique solutions.

x + 2 y = 3, 2 x + 4 y = 15

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