Solve the system by the substitution method.

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

Ask by Morgan Bradley. 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
A. The solution set is There are infinitely many solutions. (Type an ordered pair.)
C. There is no solution.

Ask by Morgan Bradley. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

We start with the system:
$$
\begin{aligned}
x - 3y &= -1 \quad \text{(1)} \
y &= -2x + 19 \quad \text{(2)}
\end{aligned}
$$

**Step 1. Substitute Equation (2) into Equation (1):**

Replace $$ y $$ in (1) with $$-2x+19$$:
$$
x - 3(-2x+19) = -1
$$

**Step 2. Simplify:**  
Distribute $$-3$$:
$$
x + 6x - 57 = -1
$$
Combine like terms:
$$
7x - 57 = -1
$$

**Step 3. Solve for $$ x $$:**  
Add 57 to both sides:
$$
7x = 56
$$
Divide both sides by 7:
$$
x = 8
$$

**Step 4. Substitute $$ x = 8 $$ back into Equation (2) to find $$ y $$:**

$$
y = -2(8) + 19 = -16 + 19 = 3
$$

Thus, the solution is the ordered pair:
$$
(8, 3)
$$

The correct choice is A. The solution set is $$ (8, 3) $$.
The solution is $$ (8, 3) $$.