Solve the system using substitution. $$ \left\{\begin{array}{l}-7 x-3 y=-45 \ -5 x+y=-29\end{array} ight. $$

Question

Solve the system using substitution. $$ \left\{\begin{array}{l}-7 x-3 y=-45 \ -5 x+y=-29\end{array}ight. $$

UpStudy AI · Accepted Answer

We start with the system:
$$
\begin{cases}
-7x - 3y = -45 \
-5x + y = -29
\end{cases}
$$

**Step 1.** Solve the second equation for $$ y $$:
$$
-5x + y = -29 \quad \Longrightarrow \quad y = -29 + 5x
$$

**Step 2.** Substitute $$ y = -29 + 5x $$ into the first equation:
$$
-7x - 3(-29 + 5x) = -45
$$

**Step 3.** Distribute the $$-3$$ in the equation:
$$
-7x + 87 - 15x = -45
$$

**Step 4.** Combine like terms:
$$
-22x + 87 = -45
$$

**Step 5.** Isolate the $$ x $$-term by subtracting $$ 87 $$ from both sides:
$$
-22x = -45 - 87 \quad \Longrightarrow \quad -22x = -132
$$

**Step 6.** Solve for $$ x $$ by dividing by $$-22$$:
$$
x = \frac{-132}{-22} = 6
$$

**Step 7.** Substitute $$ x = 6 $$ back into the expression for $$ y $$:
$$
y = -29 + 5(6) = -29 + 30 = 1
$$

The solution for the system is:
$$
x = 6, \quad y = 1
$$
$$ x = 6 $$ and $$ y = 1 $$.

Solve the system using substitution. \( \left\{\begin{array}{l}-7 x-3 y=-45 \\ -5 x+y=-29\end{array}\right. \)