What is solution ?
A straight line will contain infinitely many points. The value which satisfies the equation is known as solution. To check if the given point is a solution or not
(i) Will apply the given point into the equation
(ii) If the point is satisfying the equation, we say the point is a solution to the equation.
(ii) If the point is not satisfying the equation, we say the point is not a solution to the equation.
Determine whether the given point satisfies the given equation, or in other words the point lies on the graph of the line:
Problem 1 :
(2, 5), y = 4x - 3
Solution :
The given point is
(x, y) = (2, 5)
Substitute 2 for x and 5 for y in the given equation.
5 = 4(2) - 3
5 = 8 - 3
5 = 5
The point (2, 5) satisfies the equation. So, it is a solution and (2, 5) is on the line.
Problem 2 :
(3, -1), y = 2x - 7
Solution :
The given point is
(x, y) = (3, -1)
Substitute 3 for x and -1 for y in the given equation.
-1 = 2(3) - 7
-1 = 6 - 7
-1 = -1
The point (3, -1) satisfies the equation. So, it is a solution and (3, -1) is on the line.
Problem 3 :
(-4, 2), y = -x + 3
Solution :
The given point is
(x, y) = (-4, 2)
Substitute -4 for x and 2 for y in the given equation.
2 = 4 + 3
2 ≠ 7
The point (-4, 2) does not satisfy the equation. So, it is not a solution and (-4, 2) is not on the line.
Problem 4 :
(-1, 7), y = -2x + 5
Solution :
The given point is
(x, y) = (-1, 7)
Substitute -1 for x and 7 for y in the given equation.
7 = -2(-1) + 5
7 = 2 + 5
7 = 7
The point (-1, 7) does not satisfy the equation. So, it is not a solution.
Problem 5 :
(4, -1), y = -2x + 7
Solution :
The given point is
(x, y) = (4, -1)
Substitute 4 for x and -1 for y in the given equation.
-1 = -2(4) + 7
-1 = -8 + 7
-1 = -1
The point (4, -1) satisfies the equation. So, it is a solution.
Problem 6 :
(1, 6), y = -3x + 5
Solution :
The given point is
(x, y) = (1, 6)
Substitute 1 for x and 6 for y in the given equation.
6 = -3(1) + 5
6 = -3 + 5
6 ≠ 2
The point (1, 6) does not satisfy the equation. So, it is not a solution and (1, 6) is not lie on the line.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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