Solve the system by the substitution method.

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

Ask by Sanders Lewis. in the United States

Jan 26,2025

Question

Solve the system by the substitution method.

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

Ask by Sanders Lewis. in the United States

Jan 26,2025

UpStudy AI · Accepted Answer

To solve the system using the substitution method, follow these steps:

1. **Express one variable in terms of the other:**
   
   From the second equation:
   $$
   y = -4x + 24
   $$

2. **Substitute this expression into the first equation:**
   
   $$
   x - 2(-4x + 24) = -3
   $$
   
   Simplify:
   $$
   x + 8x - 48 = -3
   $$
   $$
   9x - 48 = -3
   $$
   
3. **Solve for $$ x $$:**
   
   $$
   9x = 45
   $$
   $$
   x = 5
   $$

4. **Substitute $$ x = 5 $$ back into the expression for $$ y $$:**
   
   $$
   y = -4(5) + 24 = -20 + 24 = 4
   $$
   
5. **Write the solution as an ordered pair:**
   
   $$
   (5, 4)
   $$

**Answer:**  
A. The solution set is $$ \{\, (5,\ 4) \,\} $$.
The solution is $$ (5, 4) $$.

Solve the system by the substitution method.

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

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Answer

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 your choice. A. The solution set is . (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Upstudy AI Solution

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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 your choice.
A. The solution set is . (Type an ordered pair.)
B. There are infinitely many solutions.
C. There is no solution.