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

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

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

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

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

Answer 1

To solve the system of equations:

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

We can use substitution or elimination. I will simplify the first equation and solve the system step by step.

### Step 1: Simplify the equations if possible

Starting with the first equation:

\[
8x - 4y = -28
\]

We can simplify it by dividing everything by 4:

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

Now we look at the second equation:

\[
2x - 6y = 8
\]

### Step 2: Solve for one variable

From Equation 1, we express \(y\) in terms of \(x\):

\[
y = 2x + 7 \quad \text{(Substituting for y)}
\]

### Step 3: Substitute into the second equation

Now substitute \(y\) into the second equation:

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

Distributing the -6:

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

Combine like terms:

\[
-10x - 42 = 8
\]

### Step 4: Solve for \(x\)

Add 42 to both sides:

\[
-10x = 50
\]

Divide by -10:

\[
x = -5
\]

### Step 5: Find \(y\)

Substitute \(x = -5\) back into Equation 1 to get \(y\):

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

\[
y = -10 + 7 = -3
\]

### Solution

The solution to the system of equations is:

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

Thus, the answer is:

\[
\text{(−5,−3)}
\]