## About "Is x y a solution to the system of equations"

Is x y a solution to the system of equations :

To check whether the given point (x, y) is a solution of the given equation, we have to follow steps given below.

Step 1 :

From the given point we have to consider the first value as x and the second value as y.

Step 2 :

Apply those values in the given equation

Step 3 :

• If the simplified value of L.H.S = R.H.S then we can decide that the given point is the solution of the given equation.
• If the simplified value of L.H.S is not equal to R.H.S then we can decide that the given point is not the solution of the given equation.

Note :

The point (x,y) lies on the given line and the given line is passing through the point (x,y) both are same.

Example 1 :

Check whether (1, 1) is a solution of the given equation 2x + 3y = 5 or not.

Solution :

x = 1 and y = 1

2x + 3y = 5

2(1) +  3(1) = 5

2 + 3 = 5

5 = 5

Since L.H.S = R.H.S, (1, 1) is the solution of the given line.

Example 2 :

Find the value of k, if x = 2 and y = 1 is a solution of the equation 2x +3 y = k.

Solution :

2(2) + 3(1) = k

4 + 3 = k

7 = k

Hence the value of k is 7.

Example 3 :

Check which of the following are solution of the equation x - 2y = 4 and which are not.

(i) (0, 2)   (ii) (2, 0) and (iii) (4, 0)

Solution :

To check whether (0, 2) is a solution or not, we have to apply the given point in the given equation.

x = 0 and y = 2

x - 2 y = 4

0 - 2(2) = 4

- 4  4

So, (0, 2) is not the solution of the given line.

To check whether (2, 0) is a solution or not, we have to apply the given point in the given equation.

x = 2 and y = 0

x - 2 y = 4

2 - 2(0) = 4

2   4

So, (2, 0) is not the solution of the given line.

To check whether (4, 0) is a solution or not, we have to apply the given point in the given equation.

x = 4 and y = 0

x - 2 y = 4

4 - 2(0) = 4

4 = 4

So, (4, 0) is the solution of the given line.

Example 4 :

Is (1, 3) a solution to this system of equations?

x + 4y = 13

5x + 4y = 17

Solution :

By applying the values x = 1, y = 3 in the first equation, we  get

x + 4y = 13

1 + 4(3) = 13

1 + 12 = 13

13 = 13

By applying the values x = 1, y = 3 in the second equation, we  get

5x + 4y = 17

5(1) + 4(3) = 17

5 + 12 = 17

17 = 17

Hence, (1, 3) is the solution of the given lines.

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