Solve the following linear system of equations: $$ 5 x+y=53 $$ $$ 3 x-9 y=3 $$ $$ x=\square $$ $$ y=\square $$

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UpStudy AI · Accepted Answer

**Step 1: Write down the equations**  
We are given the system:  
$$
5x + y = 53
$$  
$$
3x - 9y = 3
$$

**Step 2: Simplify the second equation**  
Divide the second equation by 3 to simplify:  
$$
\frac{3x - 9y}{3} = \frac{3}{3}
$$  
$$
x - 3y = 1
$$

**Step 3: Express $$ x $$ in terms of $$ y $$**  
From the simplified equation:  
$$
x - 3y = 1 \quad \Rightarrow \quad x = 3y + 1
$$

**Step 4: Substitute $$ x $$ in the first equation**  
Replace $$ x $$ in the first equation $$ 5x + y = 53 $$ with $$ 3y + 1 $$:  
$$
5(3y + 1) + y = 53
$$

**Step 5: Simplify and solve for $$ y $$**  
Expand the equation:  
$$
15y + 5 + y = 53
$$  
Combine like terms:  
$$
16y + 5 = 53
$$  
Subtract 5 from both sides:  
$$
16y = 48
$$  
Divide both sides by 16:  
$$
y = \frac{48}{16} = 3
$$

**Step 6: Substitute back to find $$ x $$**  
Use the relation $$ x = 3y + 1 $$:  
$$
x = 3(3) + 1 = 9 + 1 = 10
$$

**Final Answer:**  
$$
x = 10
$$  
$$
y = 3
$$
$$ x = 10 $$ and $$ y = 3 $$.

Solve the following linear system of equations: \( 5 x+y=53 \) \( 3 x-9 y=3 \) \( x=\square \) \( y=\square \)

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