Question

# Solve 49x + 9= 49x + 83

a)Does the equation have one solution , no solution or infinitely many solutions ?

b) Write two equations in one variable that have the same number of solutions as this equation

Hint:

### An equation where no value can be substituted for the variable which will satisfy the equation i.e. for no value of x (or any other variable in the equation), would LHS equal RHS.

Hence, an equation where LHS ≠ RHS for any value of x has no solutions.

We will simplify the given equation and check whether LHS = RHS or not.

## The correct answer is: The given equation- 49x + 9 = 49x + 83 has no solutions. Also, 3m - 87 = 3m + 87 & 700y = 700y - 100 are examples of 2 equations with the same number of solutions that the given equation has i.e. no solutions.

### Step-by-step solution:-

a). Identification of whether the given equation has one solution, no solution or infinitely many solutions:-

Simplifying the given equation i.e. 49x + 9 = 49x + 83, we get-

49x + 9 = 49x+83

∴ 49x - 49x + 9 = 49x - 49x + 83 ................................................. (Adding -49 noth the sides)

∴ 0 + 9 = 0 + 83

∴ 9 ≠ 83

∴ LHS ≠ RHS

b). 2 Equations in one variable that have the same number of solutions as the above equation i.e. 49x + 9 = 49x + 83:-

Since the given equation has no solutions, we need to give 2 examples of equations in one variable that also have no solutions.

The following equations have no solutions:-

i. 3m - 87 = 3m + 87

Simplifying the above equation, we get-

3m - 3m - 87 = 3m - 3m + 87 ...................................... (Adding -3m both sides)

∴ 0 - 87 = 0 + 87

∴ -87 ≠ 87

∴ LHS ≠ RHS

ii. 700y = 700y - 100

Simplifying the above equation, we get-

700y - 700y = 700y - 700y - 100 .................................... (Adding -700y both sides)

∴ 0 = 0 - 100

∴ 0 ≠ - 100

∴ LHS ≠ RHS

Since, for both the above equations, LHS does not equal to RHS, the 2 equations have no solutions.

Final Answer:-

∴ The given equation- 49x+9= 49x+83 has no solutions. Also, 3m - 87 = 3m + 87 & 700y = 700y - 100 are examples of 2 equations with the same number of solutions that the given equation has i.e. no solutions.

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