Solve the system of equations using elimination: and .
Answer

Ask by Summers Howell. in the United States

Jan 22,2025

Question

Solve the system of equations using elimination: $$ x-y=11 $$ and $$ 5 x+6 y=-44 $$. Answer

UpStudy AI · Accepted Answer

To solve the system of equations using the elimination method:

$$
\begin{cases}
x - y = 11 \quad \quad \quad \quad \quad (1) \
5x + 6y = -44 \quad \quad (2)
\end{cases}
$$

**Step 1: Express $$ x $$ from Equation (1)**

From equation (1):

$$
x = y + 11
$$

**Step 2: Substitute $$ x $$ into Equation (2)**

Substitute $$ x = y + 11 $$ into equation (2):

$$
5(y + 11) + 6y = -44
$$

**Step 3: Simplify and solve for $$ y $$**

$$
5y + 55 + 6y = -44 \
11y + 55 = -44 \
11y = -44 - 55 \
11y = -99 \
y = \frac{-99}{11} \
y = -9
$$

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

Substitute $$ y = -9 $$ back into the expression for $$ x $$:

$$
x = -9 + 11 \
x = 2
$$

**Solution:**

$$
x = 2 \quad \text{and} \quad y = -9
$$
$$ x = 2 $$ and $$ y = -9 $$.

Solve the system of equations using elimination: and .
Answer