`2x+4y=5x+11`
`6x-5y=-16`
What ordered pair `(x, y)` represents the solution to the system of equations above?

Answer

To solve the system of equations given by:

1. \( 2x + 4y = 5x + 11 \)
2. \( 6x - 5y = -16 \)

we will follow these steps:

### Step 1: Rearrange the first equation
We start with the first equation:

\[ 2x + 4y = 5x + 11 \]

To rearrange it, we can move all terms involving \(x\) to one side and the constant terms to the other side:

\[ 2x - 5x + 4y = 11 \]

This simplifies to:

\[ -3x + 4y = 11 \]

### Step 2: Write the first equation in standard form
Now, we can rewrite this equation in standard form:

\[ -3x + 4y = 11 \]

### Step 3: Write the second equation in standard form
The second equation is already in standard form:

\[ 6x - 5y = -16 \]

### Step 4: Eliminate one variable
We will eliminate \(x\) by manipulating both equations. To do this, we can multiply the first equation by 2 to make the coefficients of \(x\) the same:

\[ 2(-3x + 4y) = 2(11) \]

This gives us:

\[ -6x + 8y = 22 \quad \text{(Equation 3)} \]

Now we have:

1. \( -6x + 8y = 22 \) (Equation 3)
2. \( 6x - 5y = -16 \) (Equation 2)

### Step 5: Add the two equations
Now, we can add Equation 3 and Equation 2 to eliminate \(x\):

\[ (-6x + 8y) + (6x - 5y) = 22 + (-16) \]

This simplifies to:

\[ 3y = 6 \]

### Step 6: Solve for \(y\)
Now, we can solve for \(y\):

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

### Step 7: Substitute \(y\) back to find \(x\)
Now that we have \(y\), we can substitute \(y = 2\) back into one of the original equations to find \(x\). We will use the first equation:

\[ -3x + 4(2) = 11 \]

This simplifies to:

\[ -3x + 8 = 11 \]

Now, isolate \(x\):

\[ -3x = 11 - 8 \]
\[ -3x = 3 \]
\[ x = -1 \]

### Step 8: Write the ordered pair
The solution to the system of equations is the ordered pair \((x, y)\):

\[ (-1, 2) \]

### Final Answer
The ordered pair \((-1, 2)\) represents the solution to the system of equations.

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