Question

Which of the following statements are true of solving equations?

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.

(You can pick more than one)

Answer 1

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

Answer 2

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 https://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.