Solve the following paris of linear (simultaneous) equation using method of elimination by substution:
y = 4x - 7
16x - 5y = 25

Answer

To solve the given pair of linear equations using the method of elimination by substitution, follow these steps:

### Step 1: Identify the equations
We have the following equations:
1. \( y = 4x - 7 \) (Equation 1)
2. \( 16x - 5y = 25 \) (Equation 2)

### Step 2: Substitute the value of \( y \) from Equation 1 into Equation 2
We will substitute \( y \) from Equation 1 into Equation 2:
\[ 16x - 5(4x - 7) = 25 \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ 16x - 20x + 35 = 25 \]
Combine like terms:
\[ -4x + 35 = 25 \]

### Step 4: Isolate \( x \)
Next, isolate \( x \) by moving 35 to the other side:
\[ -4x = 25 - 35 \]
\[ -4x = -10 \]

### Step 5: Solve for \( x \)
Now, divide both sides by -4:
\[ x = \frac{-10}{-4} = \frac{10}{4} = \frac{5}{2} \]

### Step 6: Substitute \( x \) back into Equation 1 to find \( y \)
Now that we have \( x \), substitute it back into Equation 1 to find \( y \):
\[ y = 4\left(\frac{5}{2}\right) - 7 \]
\[ y = \frac{20}{2} - 7 \]
\[ y = 10 - 7 = 3 \]

### Final Solution
Thus, the solution to the system of equations is:
\[ x = \frac{5}{2}, \quad y = 3 \]

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