Solve the system of equations. $$ 10 x-9 y=24 $$ $$ y=x-2 $$ $$ x=\square $$ $$ y=\square $$

Question

UpStudy AI · Accepted Answer

Let's solve the system of equations step by step:

$$
\begin{cases}
10x - 9y = 24 \
y = x - 2
\end{cases}
$$

**Step 1: Substitute $$ y $$ from the second equation into the first equation.**

Given $$ y = x - 2 $$, substitute this into the first equation:

$$
10x - 9(x - 2) = 24
$$

**Step 2: Simplify and solve for $$ x $$.**

$$
10x - 9x + 18 = 24 \
x + 18 = 24 \
x = 24 - 18 \
x = 6
$$

**Step 3: Substitute $$ x = 6 $$ back into the second equation to find $$ y $$.**

$$
y = x - 2 \
y = 6 - 2 \
y = 4
$$

**Solution:**

$$
x = 6 \
y = 4
$$
$$ x = 6 $$ and $$ y = 4 $$.

Solve the system of equations.