Answered

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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 :

GinnyAnswer
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
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