Question

2x-y=4 and 3x-4y=1 solve by graphical method​

Answer 1

Answer:

hope it helps u

Step-by-step explanation:

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

The point (3,2) lies on the line 3x-4y=13x−4y=1

Explanation:

Given that the system of equations is 2x-3y=12x−3y=1 and 3x-4y=13x−4y=1

First, we shall plot the equation 2x-3y=12x−3y=1 in the graph.

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

When y=0y=0 ⇒ 2x=1\implies x=0.52x=1⟹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=12x−3y=1

Similarly, we shall plot the equation 3x-4y=13x−4y=1 in the graph.

When x=0x=0 ⇒ -4y=1\implies y=-0.25−4y=1⟹y=−0.25

When y=0y=0 ⇒ 3x=1\implies x=0.33333x=1⟹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=13x−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=12x−3y=1

Substituting (3,2) in the equation 2x-3y=12x−3y=1 , we get,

2(3)-3(2)=12(3)−3(2)=1

6-6=16−6=1

0\neq 10

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=1

Hence, the point (3,2) does not lie in the equation 2x-3y=12x−3y=1

To determine the point (3,2) lie in the equation 3x-4y=13x−4y=1

Substituting (3,2) in the equation 3x-4y=13x−4y=1 , we get,

3(3)-4(2)=13(3)−4(2)=1

9-8=19−8=1

1=11=1

Hence, the point (3,2) lie in the equation 3x-4y=13x−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.

(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