To solve the system of equations using substitution, we first write down the equations:
- \( 3x - 4y = 11 \) (Equation 1)
- \( 7x + 3y = 1 \) (Equation 2)
Step 1: Solve one of the equations for one variable
Let's solve Equation 1 for \( y \):
\[ 3x - 4y = 11 \]
Rearranging gives:
\[ -4y = 11 - 3x \]
Dividing by \(-4\):
\[ y = \frac{3x - 11}{4} \quad \text{(Equation 3)} \]
Step 2: Substitute \( y \) into the other equation
Now, we substitute Equation 3 into Equation 2:
\[ 7x + 3\left(\frac{3x - 11}{4}\right) = 1 \]
Multiply through by 4 to eliminate the fraction:
\[ 28x + 3(3x - 11) = 4 \]
Distributing gives:
\[ 28x + 9x - 33 = 4 \]
Combining like terms:
\[ 37x - 33 = 4 \]
Adding 33 to both sides:
\[ 37x = 37 \]
Dividing by 37:
\[ x = 1 \]
Step 3: Substitute \( x \) back into Equation 3 to find \( y \)
Now that we have \( x \), we can find \( y \) by substituting \( x = 1 \) into Equation 3:
\[ y = \frac{3(1) - 11}{4} = \frac{3 - 11}{4} = \frac{-8}{4} = -2 \]
Final solution
Thus, the solution to the system of equations is:
\[ x = 1 \quad \text{and} \quad y = -2 \]
You can write the final answer as:
The solution of the system is \( x = 1 \) and \( y = -2 \).