Question

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Solving Equations Using Substitution Practice
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Question
Solve the system of equations.
–9x+y=12

2x+4y= −28
(1 point)
(
,
)

Answer 1

To solve the system of equations given by:

1. \( -9x + y = 12 \) (Equation 1)
2. \( 2x + 4y = -28 \) (Equation 2)

we can use substitution or elimination. Let's use substitution for this example.

**Step 1: Solve Equation 1 for \( y \)**

From Equation 1:
\[
y = 9x + 12
\]

**Step 2: Substitute \( y \) from Equation 1 into Equation 2**

Substituting \( y \) into Equation 2:
\[
2x + 4(9x + 12) = -28
\]

**Step 3: Simplify the equation**

Expanding the equation:
\[
2x + 36x + 48 = -28
\]
\[
38x + 48 = -28
\]

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

Subtract 48 from both sides:
\[
38x = -28 - 48
\]
\[
38x = -76
\]
\[
x = -\frac{76}{38} = -2
\]

**Step 5: Substitute \( x \) back into the equation for \( y \)**

Using \( x = -2 \) in \( y = 9x + 12 \):
\[
y = 9(-2) + 12
\]
\[
y = -18 + 12
\]
\[
y = -6
\]

**Final Answer:**

The solution to the system of equations is:
\[
(x, y) = (-2, -6)
\]

So, the answer is \((-2, -6)\).