If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation
a. Changes
b. Remains the same
c. Changes in case of multiplication only
d. Changes in case of division only
Solution:
Consider a linear equation x + 2y = 5 … (1)
Substitute x = 1 in the equation
1 + 2y = 5
2y = 5 - 1
2y = 4
Dividing both sides by 2
y = 2
The solution of the equation is (1, 2)
Let us multiply equation (1) by 3
3x + 6y = 15
Substitute x = 1 and y = 2
LHS = 3 (1) + 6 (2)
= 3 + 12
= 15
= RHS
The solution remains the same by multiplying an equation with a non zero number
Now by dividing equation (1) by 2
x/2 + y = 5/2
Substitute x = 1 and y = 2 in equation (1)
LHS = 1/2 + 2
Taking LCM
= (1 + 4)/2
= 5/2
= RHS
The solution remains the same by dividing an equation with a non zero number.
Therefore, the solution remains the same.
✦ Try This: The graph of the linear equation 3x + 5y = 15 is a line which meets the x-axis at the point a. (0, 3), b. (3, 0), c. (5, 0), d. (0, 5)
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 4
NCERT Exemplar Class 9 Maths Exercise 4.1 Problem 16
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation a. Changes, b. Remains the same, c. Changes in case of multiplication only, d. Changes in case of division only
Summary:
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation remains the same
☛ Related Questions:
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