Question

Which of the following statements are true of solving equations?

Answer 1

The statement A, B and C are true for solving the equations.

Further explanation:

Given:

The statements of solving equation are as follows,

A. You are using inverse operations to isolate the variable.

B. The addition property is usually used first.

C. You are making a good guess at the solution.

D. Order of operations is often done in reverse order.

E. There are usually two solutions for a linear equation.

Explanation:

By isolate the variables we can solve the linear equation.

Consider an equation as $y + 3 = 5$.

To solve the equation isolate y.

$\begin{aligned}y&= 5 - 3\\&=2\\\end{aligned}$

Option A is true.

Now consider the two equations as $a - 3b = 4$ and $a + 3b = 8$.

We have to add the two equations to solve the equations.

 $\begin{aligned}a - 3b + a + 3b&= 4 + 8\\2a&=12\\a&=\frac{{12}}{2}\\a&= 6\\\end{aligned}$

Option B is true.

Option C is false as we cannot solve the equation by guessing the solution.

Option D is true as we can often reverse the order of the operation.

Option E is false as the linear equation can have exactly one solution or infinitely many solutions.

Hence, the statement A, B and C are true for solving the equations

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear Equation

Keywords: solving equation, inverse operation, isolate, variable, addition property, good guess, solution, order of operations, reverse order, two solution, linear equation.

Answer 2

we will check each options

option-A:

For solving any equations , we always isolate variables on anyone side

For exp: x+7=1

so, this is TRUE

option-B:

For solving system of equations

For exp:

x-y=1

x+y=3

If we use addition , we could easily solve for x and y

so, this is TRUE

option-C:

We always solve problems using conventional method

we do not guess

so, this is  FALSE

option-D:

We often reverse order of operation

For exp:

(x-2)^2-3=0

so, this is TRUE

option-E:

For linear equations , we always get one solution , infinite solutions or no solutions

so, this is FALSE