Question

24. Solve graphically the following pair of linear equations :
2x - 3y = 1, 3x - 4y = 1
Does the point (3, 2) lie on any one of the lines? Write its equation.
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Answer 1

Take a graph where you have drawn 3x-4y =1or y =3x-1/4 table at the bottom.

Answer 2

The solution of the system of equations is (-1,-1)

The point (3,2) lies on the line $3x-4y=1$

Explanation:

Given that the system of equations is $2x-3y=1$ and $3x-4y=1$

First, we shall plot the equation $2x-3y=1$ in the graph.

When $x=0$ ⇒ $-3y=1\implies y=-0.3333$

When $y=0$ ⇒ $2x=1\implies x=0.5$

Hence, plotting the coordinates (0,-0.3333) and (0.5,0) and joining the line, we get, the line for the equation $2x-3y=1$

Similarly, we shall plot the equation $3x-4y=1$ in the graph.

When $x=0$ ⇒ $-4y=1\implies y=-0.25$

When $y=0$ ⇒ $3x=1\implies x=0.3333$

Hence, plotting the coordinates (0,-0.3333) and (0.5,0) and joining the line, we get, the line for the equation $3x-4y=1$

The solution to the system of equations is the point of intersection of the two lines.

Hence, the solution is (-1,-1)

To determine the point (3,2) lie in the equation $2x-3y=1$

Substituting (3,2) in the equation $2x-3y=1$, we get,

$2(3)-3(2)=1$

        $6-6=1$

              $0\neq 1$

Hence, the point (3,2) does not lie in the equation $2x-3y=1$

To determine the point (3,2) lie in the equation $3x-4y=1$

Substituting (3,2) in the equation $3x-4y=1$, we get,

$3(3)-4(2)=1$

        $9-8=1$

              $1=1$

Hence, the point (3,2) lie in the equation $3x-4y=1$

Learn more:

(1) Solve graphically the pair of linear equations 3x - 4y + 3 = 0 and 3x + 4y- 21=0.Find the coordinates of vertices of triangular region formed by these lines and x-axis. Also calculate the area of this triangle.

brainly.in/question/3161070

(2) Question 1 Solve the following pair of linear equations by the elimination method and the substitution method:

(i) x+y=5 and 2x-3y=4 (ii) 3x+4y=10 and 2x-2y=2

(iii) 3x-5y-4=0 and 9x=2y+7 (iv) x/2 + 2y/3 = -1 and x - y/3 = 3

brainly.in/question/1345026