Question

Solve the system of equations by substitution.
left brace Start 2 By 1 Matrix 1st Row 1st Column 3 x minus 4 y equals 11 2nd Row 1st Column 7 x plus 3 y equals 1 EndMatrix

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Part 1
The solution of the system is xequals
  
enter your response here and yequals
  
enter your response here.
​(Type integers or simplified​ fractions.)

Answer 1

To solve the system of equations using substitution, we first write down the equations:

1. \( 3x - 4y = 11 \) (Equation 1)
2. \( 7x + 3y = 1 \) (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 \( y = -2 \).