Question

How do you know when an equation has one solution? A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same

Answer 1

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Define an equation with one solution

You can tell that an equation has one solution if you solve the equation and get a variable equal to a number. A system of linear equations has one solution when the graphs intersect at a point.

STEP 2: Examine the options

An equation is said to have "no solution" when the coefficients are the same and the constants are different as seen below:

`\begin{gathered} 4x+12=24+4x \\ 4x-4x=24-12 \\ 0=12 \end{gathered}`

When the coefficients are the same and the constants are the same, the equation is said to have "infinitely many solutions as seen below:

`\begin{gathered} 4x-14=-6-8+4x \\ 4x-14=-14+4x \\ 4x-4x=-14+14 \\ 0=0 \end{gathered}`

When the coefficients are different, the equation is said to have one solution as seen below:

`\begin{gathered} 2x+56=3x-12 \\ 2x-3x=-12-56 \\ -x=-68 \\ x=68 \end{gathered}`

Hence, the answer is:

"When the coefficients are different"