Questions: What is the value of y in the solutions of the system of equations: 3x+4y= 3 and 2x-4y=12? (Suggest using the Addition Method)

What is the value of y in the solutions of the system of equations: 3x+4y= 3 and 2x-4y=12? (Suggest using the Addition Method)
Transcript text: What is the value of $y$ in the solutions of the system of equations: $3 x+4 y=$ 3 and $2 x-4 y=12$ ? (Suggest using the Addition Method)
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Solution

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Solution Steps

Step 1: Write Down the System of Equations

We are given the following system of equations:

  1. \(3x + 4y = 3\)
  2. \(2x - 4y = 12\)
Step 2: Add the Equations to Eliminate \(y\)

To eliminate \(y\), we can add the two equations together. Notice that the coefficients of \(y\) in the two equations are \(+4\) and \(-4\), which will cancel each other out when added.

\[ (3x + 4y) + (2x - 4y) = 3 + 12 \]

Simplifying the left side, we get:

\[ 3x + 2x + 4y - 4y = 15 \]

This simplifies to:

\[ 5x = 15 \]

Step 3: Solve for \(x\)

Divide both sides of the equation by 5 to solve for \(x\):

\[ x = \frac{15}{5} = 3 \]

Step 4: Substitute \(x\) Back into One of the Original Equations

Now that we have \(x = 3\), substitute this value back into one of the original equations to solve for \(y\). Let's use the first equation:

\[ 3x + 4y = 3 \]

Substitute \(x = 3\):

\[ 3(3) + 4y = 3 \]

Simplify:

\[ 9 + 4y = 3 \]

Step 5: Solve for \(y\)

Subtract 9 from both sides:

\[ 4y = 3 - 9 \]

\[ 4y = -6 \]

Divide both sides by 4:

\[ y = \frac{-6}{4} = -\frac{3}{2} \]

Final Answer

The value of \(y\) in the solution of the system of equations is:

\[ \boxed{y = -\frac{3}{2}} \]

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