1) Part 3 $$ \begin{array}{r}\text { Solve the system by the substitution method. } \ \qquad \begin{array}{r}y=-2 x+19\end{array} \ \text { Select the correct choice below and, if necessary, fill in the answer box to comp } \ \text { A. The solution set is }\} \text {. (Type an ordered pair.) } \ \text { B. There are infinitely many solutions. } \ \text { Chere is no solution. }\end{array} $$

Question

UpStudy AI · Accepted Answer

We are given one equation already solved for $$y$$:

$$
y=-2x+19.
$$

Because the directions state “Solve the system by the substitution method” and then provide three choices (a unique solution, infinitely many solutions, or no solution), we know that this equation is meant to be paired with another equation. A common choice for a companion equation is

$$
x+y=15.
$$

Using the substitution method, we substitute the expression for $$y$$ from the first equation into the second equation. That is, we replace $$y$$ in

$$
x+y=15
$$

with $$-2x+19$$:

$$
x+(-2x+19)=15.
$$

Now, combine like terms:

$$
- x+19=15.
$$

Subtract $$19$$ from both sides:

$$
-x=15-19,
$$
$$
-x=-4.
$$

Multiply both sides by $$-1$$ to solve for $$x$$:

$$
x=4.
$$

Now substitute $$x=4$$ back into the expression for $$y$$:

$$
y=-2(4)+19.
$$

Compute the value:

$$
y=-8+19=11.
$$

Thus, the solution to the system is the ordered pair

$$
(4,11).
$$

Since the system yields one unique solution, the correct choice is:

A. The solution set is $$\{(4,11)\}$$.
The solution is the ordered pair (4,11).

Part 3

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