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)

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)

Solution

Solution Steps

Step 1: Write Down the System of Equations

We are given the following system of equations:

$3x + 4y = 3$
$2x - 4y = 12$

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 $x = 3$: