Question

Solve graphically.
x - 2y = 5 , 2x - 4y = 10
​

Answer 1

Answer:

Both the equation coincide and has infinitely many solutions.

Step-by-step explanation:

Given: The equations are x - 2y = 5 , 2x - 4y = 10

To find: Solve the equation by graphically

Solution:

The equation are

The given equation are

x - 2y = 5                (1)

2x - 4y = 10            (2)

Find the table of values for the  equation x - 2y = 5      

y = $\frac{x-5}{2}$

Let sub x= 1 in eq (1)

y = $\frac{x-5}{2}$

y = $\frac{1 - 5}{2}$

y = -2

(x,y) = (1 , -2)

x = 3

y = $\frac{x-5}{2}$

y = $\frac{3- 5}{2}$

y =- 1

(x,y) = ( 3, -1)

x = 5

y = $\frac{x-5}{2}$

y = $\frac{5- 5}{2}$

y =-0

(x,y) = (5,0)

The table value of x,y

x     1      3     5

y    -2    -1     0

Find the table of values for the equation 2x - 4y = 10

y = $\frac{2x - 10}{4}$

y  =$\frac{x - 5}{2}$

Let sub x= 1 in eq (1)

y = $\frac{x-5}{2}$

y = $\frac{1 - 5}{2}$

y = -2

(x,y) = (1 , -2)

x = 3

y = $\frac{x-5}{2}$

y = $\frac{3- 5}{2}$

y =- 1

(x,y) = ( 3, -1)

x = 5

y = $\frac{x-5}{2}$

y = $\frac{5- 5}{2}$

y =-0

(x,y) = (5,0)

The table value of x,y

x     1      3     5

y    -2    -1     0

Both values are same and coincide.

Therefore there are infinitely many solutions

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Answer 2

Answer:

Graph for x - 2y = 5 and 2x -4y = 10 is given below.

Step-by-step explanation:

Explanation:

x - 2y = 5 and 2x - 4y = 10

As we know that, in order to solve the problem graphically, function graphs must be plotted in a single coordinate plane and intersection points must be sought after.

So, first we find the points for each equation.

Step 1:

For x - 2y = 5

On putting x = 0 then y = $\frac{-5}{2}$ = -2.5

On putting y = 0 then x = 5

So, the points are (0,-2.5 ) and (5, 0)

For 2x - 4y = 10

On putting x = 0 then y = $\frac{-10}{4} = \frac{-5}{2}$ = -2.5

On putting y = 0 then x = $\frac{10}{2}$ = 5

So, the points are (0 , -2.5) and(5 , 0)

Table for x and y :

x   0         5

y  -2.5      0

Final answer:

Hence, graph for the given equation is given below.

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