Daniel Byrd
04/02/2023 · High School
\( \left\{ \begin{array} { l } { 2 x - 3 } \\ { 4 x + 5 } \end{array} \right. \)
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Tutor-Verified Answer
Step-by-step Solution
To solve the system of equations:
\[
\begin{align*}
2x - 3 &= 0 \\
4x + 5 &= 0
\end{align*}
\]
We can solve each equation separately.
For the first equation:
\[
2x - 3 = 0
\]
Add 3 to both sides:
\[
2x = 3
\]
Divide both sides by 2:
\[
x = \frac{3}{2}
\]
For the second equation:
\[
4x + 5 = 0
\]
Subtract 5 from both sides:
\[
4x = -5
\]
Divide both sides by 4:
\[
x = -\frac{5}{4}
\]
So, the solutions to the system of equations are:
\[
x = \frac{3}{2} \quad \text{and} \quad x = -\frac{5}{4}
\]
However, since the two equations are not the same, they do not have a single solution that satisfies both equations simultaneously. Instead, they represent two different lines on a graph, and there is no point where they intersect. Therefore, the system has no solution.
Quick Answer
The system of equations has no solution.
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