IS X Y A SOLUTION TO THE SYSTEM OF EQUATIONS
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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