Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Tyler Simpson. in the United States

Mar 23,2025

Question

Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Tyler Simpson. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

1. Given the system of equations:
   $$
   \begin{aligned}
   x + 3y &= -1 \quad (1) \
   y &= -2x - 12 \quad (2)
   \end{aligned}
   $$

2. Substitute equation (2) into equation (1):
   $$
   x + 3(-2x - 12) = -1
   $$

3. Simplify the equation:
   $$
   x - 6x - 36 = -1
   $$
   $$
   -5x - 36 = -1
   $$

4. Solve for $$ x $$:
   $$
   -5x = 35 \quad \Rightarrow \quad x = -7
   $$

5. Substitute $$ x = -7 $$ back into equation (2) to solve for $$ y $$:
   $$
   y = -2(-7) - 12
   $$
   $$
   y = 14 - 12
   $$
   $$
   y = 2
   $$

6. The solution to the system is:
   $$
   (x,y) = (-7, 2)
   $$

Thus, the correct choice is A: The solution set is $$ \{(-7,2)\} $$.
The solution is $$ (-7, 2) $$, so choice A is correct.

Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.

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Solve the system by the substitution method. Select the correct choice below and, if necessary, fill in the answer box to complete A. The solution set is . (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

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Solve the system by the substitution method.

Select the correct choice below and, if necessary, fill in the answer box to complete
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.