Question

Please help.
For the equations given below, which statement is true?

A) The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
B) The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
C) The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation.
D) The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation.

Answer 1

hope so if we subtract 6 in second equation then both the equation will become same so the solution will also become same

Answer 2

Answer:  The correct option is

(A) The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

Step-by-step explanation:  The given linear equations in one unknown variable are as follows:

-3x - 8 = 19                                       (i)

-3x - 2 = 25                                      (ii)

We are given to select the correct statement about the above the solutions of the two equations.

We know that any two equations in one variable will have same solution if one can be obtained from the other by adding, subtracting, multiplying or dividing by a constant.

We have, after adding 6 to equation (i) that

   (-3x - 8) + 6 = 19 + 6

⇒ -3x - 8 + 6 = 25

⇒ -3x -2 = 25, which is equation (ii).

Solving equation (i), we get

  -3x - 8 = 19

⇒  -3x = 27

⇒ x = -9,

and solving equation (ii), we get

-3x - 2 = 25

⇒  -3x = 27

⇒ x = -9.

Thus, equations have same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

Option (A) is correct.