Question

verify whether the system of given linear equation as in a unique solution or not 2x+3y-7=0 6x+5y-11=0

Answer 1

do that for your answer

Answer 2

The given system of equations has unique solution.

Given,

System of given linear equations:

2x + 3y - 7 = 0,

6x + 5y - 11 = 0.

To find,

Whether the system of given linear equations has unique solution or not.

Solution,

We can see that the given system of linear equations is as follows.

2x + 3y - 7 = 0, and

6x + 5y - 11 = 0.

Now, when a system of linear equations is such that the equations are

$a_1x+b_1y+c_1=0,\\a_2x+b_2y+c_2=0.$

Then, the above system of equations has

• A unique solution, if $\frac{a_1}{a_2} \neq\frac{b_1}{b_2}$,
• No solution, if $\frac{a_1}{a_2} =\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$,
• Infinitely many solutions, if $\frac{a_1}{a_2} =\frac{b_1}{b_2} = \frac{c_1}{c_2}$.

Here, we can see that

$\frac{a_1}{a_2} =\frac{2}{6}=\frac{1}{3}$ and

$\frac{b_1}{b_2}=\frac{3}{5}$

Since $\frac{1}{3} \neq \frac{3}{5}$

Thus,

$\frac{a_1}{a_2} \neq\frac{b_1}{b_2}$

⇒ the condition for unique solution is satisfied.

Therefore, the given system of equations has unique solution.

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