State whether the following statement is true or false.

Point (-2, -5) is the solution of the linear equation $3 x - 5 y = 19 : - 7 x + 3 y + 1 = 0$ .

And point (4,9) lies on the linear equation $- 7 x + 3 y + 1 = 0$ .

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given pair of linear equations:

3 x - 5 y = 19 or 3 x - 5 y − 19 = 0 … . 1 3 y - 7 x + 1 = 0 or − 7 x + 3 y + 1 = 0 … . 2

Constructing a suitable table with at least two Solutions for each equation in order to produce a graphical representation:
From equation (1),

y = 3 x − 19 5

Then table for

3 x − 5 y − 19 = 0

is,

We get,

0, − 3.8

6.33, 0

and

− 2, − 5

.
And
From equation (2),

y = 7 x − 1 3

Then table for

− 7 x + 3 y + 1 = 0

is,

We get,

1, 2

0, − 0.33

and

4, 9

.
Then,
Create a graph of both equations using the same scale of representation and the same graph paper:
We get the graph for the given equations by drawing points

0, − 3.8

6.33, 0

− 2, − 5

1, 2

0, − 0.33

and

4, 9

on graph paper and connecting them with lines.

In the graph, we observed that these two lines intersect at point (- 2, - 5).

\Rightarrow

we get the graphical representation of the given equation.
Hence, (- 2, - 5) is the solution of the given equations and yes, point (4, 9) lies on the equation