Solve for the values of x and y in the following system: $$ 4x - y = 7 $$ and $$ 2x + 5y = 11 $$

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UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
4x - y = 7 \quad \text{(Equation 1)} \
2x + 5y = 11 \quad \text{(Equation 2)}
\end{cases}
$$

**Step 1: Solve Equation 1 for $$ y $$**

From Equation 1:
$$
4x - y = 7 \
\Rightarrow y = 4x - 7
$$

**Step 2: Substitute $$ y $$ into Equation 2**

Plugging $$ y = 4x - 7 $$ into Equation 2:
$$
2x + 5(4x - 7) = 11 \
2x + 20x - 35 = 11 \
22x - 35 = 11
$$

**Step 3: Solve for $$ x $$**
$$
22x = 11 + 35 \
22x = 46 \
x = \frac{46}{22} \
x = \frac{23}{11}
$$

**Step 4: Find $$ y $$ using the value of $$ x $$**

Substitute $$ x = \frac{23}{11} $$ back into $$ y = 4x - 7 $$:
$$
y = 4\left(\frac{23}{11}\right) - 7 \
y = \frac{92}{11} - \frac{77}{11} \
y = \frac{15}{11}
$$

**Solution:**
$$
x = \frac{23}{11}, \quad y = \frac{15}{11}
$$

**Decimal Approximation:**
$$
x \approx 2.09, \quad y \approx 1.36
$$
$$ x = \frac{23}{11} $$ and $$ y = \frac{15}{11} $$.

Solve for the values of x and y in the following system: \( 4x - y = 7 \) and \( 2x + 5y = 11 \)

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