Question

How many solutions does an equation have when the variable adds out and the final sentence is true?

Answer 1

Infinitely many solutions

Step-by-step explanation:

If we have a system of equation like:

2x+y=4

6x+3y=12

If we make y the subject in the first equation and substitute into the second equation, we get:

6x+3(4-2x)=12

We expand to get:

6x+12-6x=12

6x-6x+12=12

Now the variable adds out to give:

12=12

This statement is true so the equation has infinitely many solution.

Answer 2

• infinite solutions

Step-by-step explanation:

When the variable adds out means that after all the simplifications, at the end, it will not appear in the final sentence or expression.

Then, if the final sentence is true, and not variable appears, but only constants, the sentence is always true, no matter what value the variable takes.

That means that you can put any value for the variable in the original equation and the equation will be true; hence there are infinite solutions.

This is an example:

1. Equation:

• 3x + 5+ x² = 2 - ( - 4x - x²) + (3 - x)

2. Remove the parenthesis:

• 3x + 5+ x² = 2 + 4x + x² + 3 - x

3. Add like terms on the right side and transpose the variables to the left side:

• 3x + 5 + x² = 5 + 3x + x²

• 3x + x² - 3x -x² + 5 = 5

4. Combine like terms on the left side:

• 5 = 5

Thus, the variable added out and the final sentence is true. Hence, this equation has infinite solutions, which you can prove substituting the variable with any value.