19) Solve the system by substitution. $$ \left\{\begin{array}{l}y=3 x+1 \ y=5 x-3\end{array} ight. $$

Question

19) Solve the system by substitution. $$ \left\{\begin{array}{l}y=3 x+1 \ y=5 x-3\end{array}ight. $$

UpStudy AI · Accepted Answer

To solve the system of equations by substitution:

$$
\begin{cases}
y = 3x + 1 \
y = 5x - 3
\end{cases}
$$

**Step 1:** Since both equations are equal to $$ y $$, set them equal to each other:

$$
3x + 1 = 5x - 3
$$

**Step 2:** Solve for $$ x $$:

$$
3x + 1 = 5x - 3 \
1 + 3 = 5x - 3x \
4 = 2x \
x = 2
$$

**Step 3:** Substitute $$ x = 2 $$ back into one of the original equations to find $$ y $$. Using the first equation:

$$
y = 3(2) + 1 \
y = 6 + 1 \
y = 7
$$

**Solution:** The system has a unique solution at $$ (x, y) = (2, 7) $$.
The solution is $$ x = 2 $$ and $$ y = 7 $$.

19) Solve the system by substitution. \( \left\{\begin{array}{l}y=3 x+1 \\ y=5 x-3\end{array}\right. \)