Solve the equations `4x + 3y = 9 and x + y = 2` for x and y.

Options

A. `x =3, y =-1`
B. `x =1, y =-3`
C. `x =3, y =2`
D. `x =-1, y =3`

Answer

To solve the equations \(4x + 3y = 9\) and \(x + y = 2\), we can follow these steps:

### Step 1: Write down the equations
We have the following two equations:
1. \(4x + 3y = 9\) (Equation 1)
2. \(x + y = 2\) (Equation 2)

### Step 2: Express one variable in terms of the other
From Equation 2, we can express \(y\) in terms of \(x\):
\[ y = 2 - x \]

### Step 3: Substitute \(y\) in Equation 1
Now, substitute \(y\) in Equation 1:
\[ 4x + 3(2 - x) = 9 \]

### Step 4: Simplify the equation
Distributing \(3\) in the equation gives:
\[ 4x + 6 - 3x = 9 \]
Now combine like terms:
\[ (4x - 3x) + 6 = 9 \]
This simplifies to:
\[ x + 6 = 9 \]

### Step 5: Solve for \(x\)
Now, isolate \(x\):
\[ x = 9 - 6 \]
\[ x = 3 \]

### Step 6: Substitute \(x\) back to find \(y\)
Now that we have \(x\), we can find \(y\) by substituting \(x\) back into the expression for \(y\):
\[ y = 2 - x = 2 - 3 = -1 \]

### Step 7: Write the solution
Thus, the solution to the equations is:
\[ x = 3, \quad y = -1 \]