Find any two solutions of the equation 4x + 3y = 12

Answer

To find two solutions of the equation \(4x + 3y = 12\), we can choose different values for \(x\) or \(y\) and solve for the other variable.

### Step 1: Choose a value for \(x\)
Let's start by choosing \(x = 0\).

### Step 2: Substitute \(x = 0\) into the equation
Substituting \(x = 0\) into the equation:
\[ 4(0) + 3y = 12 \]
This simplifies to:
\[ 3y = 12 \]

### Step 3: Solve for \(y\)
Now, divide both sides by 3:
\[ y = \frac{12}{3} = 4 \]
So, one solution is \((0, 4)\).

### Step 4: Choose another value for \(x\)
Now, let's choose \(x = 3\).

### Step 5: Substitute \(x = 3\) into the equation
Substituting \(x = 3\) into the equation:
\[ 4(3) + 3y = 12 \]
This simplifies to:
\[ 12 + 3y = 12 \]

### Step 6: Solve for \(y\)
Now, subtract 12 from both sides:
\[ 3y = 12 - 12 \]
\[ 3y = 0 \]
Now, divide both sides by 3:
\[ y = 0 \]
So, the second solution is \((3, 0)\).

### Final Solutions
The two solutions we found are:
1. \((0, 4)\)
2. \((3, 0)\)