Answered

Get expert insights and reliable answers to your questions on IDNLearn.com. Find accurate and detailed answers to your questions from our experienced and dedicated community members.

What is the solution to the system of equations?

[tex]\[
\begin{cases}
2x - y = 7 \\
y = 2x + 3
\end{cases}
\][/tex]

A. (2, 3)

B. (2, 7)

C. No solution

D. Infinite number of solutions

Sagot :

GinnyAnsweridn
To solve the given system of equations, we can use substitution or elimination. We will use substitution in this case.

Given equations are:

1. [tex]\( 2x - y = 7 \)[/tex]
2. [tex]\( y = 2x + 3 \)[/tex]

### Step-by-Step Solution:

1. First, we will substitute the value of [tex]\( y \)[/tex] from the second equation [tex]\( y = 2x + 3 \)[/tex] into the first equation [tex]\( 2x - y = 7 \)[/tex].

[tex]\[ 2x - (2x + 3) = 7 \][/tex]

2. Now, simplify the equation:

[tex]\[ 2x - 2x - 3 = 7 \][/tex]

3. This simplifies further to:

[tex]\[ -3 = 7 \][/tex]

4. Since [tex]\(-3 = 7\)[/tex] is a contradiction (it is not true), there is no value of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that can satisfy both equations simultaneously.

### Conclusion:

Given the contradiction we reached, there is no solution to this system of equations.

Therefore, the correct answer is:

no solution
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.