Systems of Linear Equations Online Practice

Question

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10 of 1310 of 13 Items

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:

\[ \text{(−5,−3)} \]