Questions: Solve the system using addition/elimination method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options.
3x-3y=-21
x+3y=5
One solution:
No solution
Infinite number of solutions
Transcript text: Solve the system using addition/elimination method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options.
\[
\left\{\begin{array}{l}
3 x-3 y=-21 \\
x+3 y=5
\end{array}\right.
\]
One solution: $\square$
No solution
Infinite number of solutions
Solution
Solution Steps
To solve the system of equations using the addition/elimination method, we aim to eliminate one of the variables by adding the equations. First, we can add the two equations directly to eliminate \( y \). If the resulting equation provides a valid solution for \( x \), we substitute back to find \( y \). If the equations result in a contradiction, there is no solution. If they result in a tautology, there are infinite solutions.
Step 1: Write the System of Equations
We start with the given system of equations:
\[
\begin{align*}
& \quad 3x - 3y = -21 \\
& \quad x + 3y = 5
\end{align*}
\]
Step 2: Solve for One Variable
Using the elimination method, we can manipulate the equations to eliminate one variable. We can multiply the second equation by 3 to align the coefficients of \( y \):
\[
3(x + 3y) = 3(5) \implies 3x + 9y = 15
\]