Question

Systems of Linear Equations Online Practice
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Question
Solve the system of equations.
8x−4y=−28

2x−6y=8
(1 point)
Responses

(−2, 3)
left parenthesis negative 2 comma 3 right parenthesis

(−4,−1)
left parenthesis negative 4 comma negative 1 right parenthesis

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

(7, 1)
left parenthesis 7 comma 1 right parenthesis

Answer 1

To solve the system of equations

1) \( 8x - 4y = -28 \)
2) \( 2x - 6y = 8 \)

let's simplify and solve them step by step.

### Step 1: Simplify the first equation
Divide the entire first equation by 4:

\[
2x - y = -7 \quad \text{(Equation 1)}
\]

### Step 2: Rewrite the second equation for clarity
The second equation is already in a suitable form:

\[
2x - 6y = 8 \quad \text{(Equation 2)}
\]

### Step 3: Solve Equation 1 for \(y\)
From Equation 1:

\[
y = 2x + 7
\]

### Step 4: Substitute \(y\) in Equation 2
Now, substitute \(y\) from Equation 1 into Equation 2:

\[
2x - 6(2x + 7) = 8
\]

### Step 5: Distribute and simplify
Distributing -6 into \(2x + 7\):

\[
2x - 12x - 42 = 8
\]

Combine like terms:

\[
-10x - 42 = 8
\]

### Step 6: Isolate \(x\)
Add 42 to both sides:

\[
-10x = 50
\]

Now divide by -10:

\[
x = -5
\]

### Step 7: Substitute \(x\) back to find \(y\)
Substituting \(x = -5\) into \(y = 2x + 7\):

\[
y = 2(-5) + 7 = -10 + 7 = -3
\]

### Final Solution
So the solution to the system of equations is:

\[
(x, y) = (-5, -3)
\]

### Checking the Options:
This matches with the option:

\[
(−5,−3) \quad \text{(left parenthesis negative 5 comma negative 3 right parenthesis)}
\]

Thus, the correct answer is **(−5,−3)**.