Question 1
Solve the system by elimination.
\[
\left\{\begin{array}{l}
-2 x-4 y=-6 \\
4 x+4 y=-4
\end{array}\right.
\]
No solution
Infinite number of solutions
Question Help:
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Answer
Final Answer: The solution to the system of equations is \(\boxed{x = -5}\) and \(\boxed{y = 4}\).
Step 1 ：The system of equations is given by: \[\left\{\begin{array}{l} -2 x-4 y=-6 \\ 4 x+4 y=-4 \end{array}\right.\]
Step 2 ：We can solve this system by elimination. This involves adding or subtracting the equations in order to eliminate one of the variables, making it possible to solve for the other variable.
Step 3 ：In this case, adding the two equations will eliminate the variable y.
Step 4 ：After finding the value of x, we can substitute it into one of the equations to find the value of y.
Step 5 ：If the system has no solution or an infinite number of solutions, it will become apparent during this process.
Step 6 ：The solution to the system of equations is \(x = -5\) and \(y = 4\).
Step 7 ：This means that the system has a unique solution, and does not have no solution or an infinite number of solutions.
Step 8 ：Final Answer: The solution to the system of equations is \(\boxed{x = -5}\) and \(\boxed{y = 4}\).
