Solve the system of equations. $$ \begin{array}{l}y=4 x+1 \ 3 x+2 y=13\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
y = 4x + 1 \quad \text{(Equation 1)} \
3x + 2y = 13 \quad \text{(Equation 2)}
\end{cases}
$$

**Step 1: Substitute Equation 1 into Equation 2**

Since Equation 1 gives $$ y $$ in terms of $$ x $$, we can substitute $$ y = 4x + 1 $$ into Equation 2.

$$
3x + 2(4x + 1) = 13
$$

**Step 2: Simplify the Equation**

Expand the terms:

$$
3x + 8x + 2 = 13
$$

Combine like terms:

$$
11x + 2 = 13
$$

**Step 3: Solve for $$ x $$**

Subtract 2 from both sides:

$$
11x = 11
$$

Divide both sides by 11:

$$
x = 1
$$

**Step 4: Substitute $$ x $$ back into Equation 1 to find $$ y $$**

$$
y = 4(1) + 1 = 4 + 1 = 5
$$

**Solution:**

$$
x = 1 \
y = 5
$$

So, the solution to the system of equations is $$ x = 1 $$ and $$ y = 5 $$.
The solution is $$ x = 1 $$ and $$ y = 5 $$.

Solve the system of equations. \( \begin{array}{l}y=4 x+1 \\ 3 x+2 y=13\end{array} \)