Question

Systems of Linear Equations Online Practice
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Question
Solve the system of equations.
x−3y=18

7x−5y=46
(1 point)
Responses

(105, 5)
left parenthesis 105 comma 5 right parenthesis

(33, 5)
left parenthesis 33 comma 5 right parenthesis

(3, −5)
left parenthesis 3 comma negative 5 right parenthesis

(−3, −5)
left parenthesis negative 3 comma negative 5 right parenthesis

Answer 1

To solve the given system of equations:

1. \( x - 3y = 18 \) (Equation 1)
2. \( 7x - 5y = 46 \) (Equation 2)

Let's solve these equations step by step.

### Step 1: Solve for \( x \) in terms of \( y \) using Equation 1.
From Equation 1:
\[ x = 3y + 18 \]

### Step 2: Substitute \( x \) into Equation 2.
Substituting \( x \) in Equation 2 gives:
\[ 7(3y + 18) - 5y = 46 \]

### Step 3: Expand and simplify.
\[ 21y + 126 - 5y = 46 \]
Combine like terms:
\[ 16y + 126 = 46 \]

### Step 4: Solve for \( y \).
Subtract 126 from both sides:
\[ 16y = 46 - 126 \]
\[ 16y = -80 \]
\[ y = -5 \]

### Step 5: Substitute \( y \) back into Equation 1 to find \( x \).
Now substitute \( y = -5 \) back into the equation for \( x \):
\[ x = 3(-5) + 18 \]
\[ x = -15 + 18 \]
\[ x = 3 \]

### Final Solution
So, the solution of the system of equations is:
\[ (x, y) = (3, -5) \]

### Answer
The correct response is:
**(3, -5)**