Question

describe nature of solution 3x-4y=0 ,5x+y=5​

Answer 1

Answer:

Nature of solution of equations 3x - 4y = 0 and 5x + y = 5 is consistent, one and only one solution and intersecting lines.

Hope it helps you.

Answer 2

Answer:

The nature of the given system of linear equations is consistent

Step-by-step explanation:

• The nature of the solution means that whether it is consistent or inconsistent
• Consistent means unique or infinitely many solutions and inconsistent means no-solution
• Let us solve the given system of linear equations by the substitution method

Step 1:

Given that

3x-4y=0

⇒ 3x = 4y

⇒ x = $\frac{4y}{3}$

Step 2:

Substitute the value of x in 5x + y = 5

We get

$5*\frac{4y}{3} +y=5$

⇒ $\frac{20y}{3} +y=5$

⇒ $\frac{20y+3y}{3} =5$

⇒ $23y=15$

⇒$y=\frac{15}{23}$

Now obtain the value of x by substituting the value of y in x = $\frac{4y}{3}$

we get

$x=\frac{4*15}{3*23}$

⇒ $x=\frac{20}{23}$

Since x comes out to be  $\frac{20}{23}$ and y comes out to be $\frac{15}{23}$, hence we have a unique value for x and y which means the given system is consistent