Answered

Solve the system of equations by the addition method.

[tex]\[
\left\{
\begin{array}{l}
x + y = -3 \\
x - y = 9
\end{array}
\right.
\][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is [tex]\(\{\square\}\)[/tex]. (Type an ordered pair.)

B. There are infinitely many solutions. The solution set is [tex]\(\{(x, y) \mid \square\}\)[/tex]. (Type an equation.)

C. There is no solution. The solution set is [tex]\(\varnothing\)[/tex].



Answer :

GinnyAnswer
Let's solve the given system of equations using the addition method. The system of equations is:

[tex]\[ \left\{ \begin{array}{l} x + y = -3 \\ x - y = 9 \end{array} \right. \][/tex]

Step 1: Add the two equations to eliminate [tex]\( y \)[/tex]

[tex]\[ (x + y) + (x - y) = -3 + 9 \][/tex]

Simplify the left-hand side:

[tex]\[ x + x + y - y = -3 + 9 \][/tex]

Combine like terms:

[tex]\[ 2x = 6 \][/tex]

Step 2: Solve for [tex]\( x \)[/tex]

[tex]\[ 2x = 6 \implies x = \frac{6}{2} \implies x = 3 \][/tex]

Step 3: Substitute [tex]\( x = 3 \)[/tex] into one of the original equations to solve for [tex]\( y \)[/tex]

We can use the first equation [tex]\( x + y = -3 \)[/tex]:

[tex]\[ 3 + y = -3 \][/tex]

Solve for [tex]\( y \)[/tex]:

[tex]\[ y = -3 - 3 \implies y = -6 \][/tex]

Conclusion:

The solution to the system of equations is the ordered pair [tex]\( (3, -6) \)[/tex].

So, the correct choice is:

A. The solution set is [tex]\( \{ (3, -6) \} \)[/tex].

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