Solve the system by the substitution method.

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

Ask by Montgomery Higgins. in the United States

Mar 25,2025

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

Ask by Montgomery Higgins. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

We are given the system
$$
\begin{aligned}
x-2y &= -1 \quad (1)\
y &= -2x+13 \quad (2)
\end{aligned}
$$

Substitute $$ y = -2x+13 $$ from equation (2) into equation (1):

$$
x - 2(-2x+13) = -1
$$

Distribute the $$-2$$:

$$
x + 4x - 26 = -1
$$

Combine like terms:

$$
5x - 26 = -1
$$

Add 26 to both sides:

$$
5x = 25
$$

Divide both sides by 5:

$$
x = 5
$$

Now, substitute $$ x = 5 $$ into equation (2) to find $$ y $$:

$$
y = -2(5)+13 = -10+13 = 3
$$

The solution to the system is the ordered pair:

$$
(5,3)
$$
The solution set is $$ (5, 3) $$.