Multiple Choice
Use the elimination method to solve the following system of linear equations.
5. Systems of Linear Equations
Solving Systems of Linear Equations by Elimination
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Determine if substitution or elimination would be more convenient to use for the system below.
A
Substitution
B
Elimination
Verified step by step guidance1
Step 1: Examine the given system of equations:
\[\{ \begin{cases} 3x + y = -3 \\ 2y = -2x \end{cases} \]
Step 2: Look for an equation that can be easily solved for one variable. The second equation, \[2y = -2x\], can be simplified by dividing both sides by 2, giving \[y = -x\].
Step 3: Since the second equation is already solved for \[y\], substitution is convenient because you can directly substitute \[y = -x\] into the first equation.
Step 4: Substitute \[y = -x\] into the first equation \[3x + y = -3\] to get \[3x + (-x) = -3\], which simplifies to \[2x = -3\].
Step 5: From here, you can solve for \[x\] easily, and then use the value of \[x\] to find \[y\] using \[y = -x\].
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