Solve graphically the following pairs of equations :
`3x+7y=27`
`8-y=5/2x`

Answer

To solve the given pair of equations graphically, we will follow these steps:

### Step 1: Write the equations
The equations given are:
1. \( 3x + 7y = 27 \)
2. \( 8 - y = \frac{5}{2}x \)

### Step 2: Convert the second equation to standard form
We can rearrange the second equation to a more standard form:
\[ 8 - y = \frac{5}{2}x \implies -y = \frac{5}{2}x - 8 \implies y = -\frac{5}{2}x + 8 \]
Now we have:
1. \( 3x + 7y = 27 \)
2. \( y = -\frac{5}{2}x + 8 \)

### Step 3: Find points for the first equation
Let's find some points for the first equation \( 3x + 7y = 27 \) by substituting different values of \( x \):

- **For \( x = 2 \)**:
\[ 3(2) + 7y = 27 \implies 6 + 7y = 27 \implies 7y = 21 \implies y = 3 \]
So, one point is \( (2, 3) \).

- **For \( x = -5 \)**:
\[ 3(-5) + 7y = 27 \implies -15 + 7y = 27 \implies 7y = 42 \implies y = 6 \]
So, another point is \( (-5, 6) \).

### Step 4: Find points for the second equation
Now, let's find some points for the second equation \( y = -\frac{5}{2}x + 8 \):

- **For \( x = 2 \)**:
\[ y = -\frac{5}{2}(2) + 8 = -5 + 8 = 3 \]
So, the point is \( (2, 3) \).

- **For \( x = 4 \)**:
\[ y = -\frac{5}{2}(4) + 8 = -10 + 8 = -2 \]
So, another point is \( (4, -2) \).

### Step 5: Plot the points on a graph
Now we will plot the points we found:
- From the first equation: \( (2, 3) \) and \( (-5, 6) \)
- From the second equation: \( (2, 3) \) and \( (4, -2) \)

### Step 6: Draw the lines
Draw a line through the points \( (2, 3) \) and \( (-5, 6) \) for the first equation, and a line through the points \( (2, 3) \) and \( (4, -2) \) for the second equation.

### Step 7: Identify the intersection point
The lines will intersect at the point \( (2, 3) \).

### Conclusion
Thus, the solution to the system of equations is:
\[ x = 2, \quad y = 3 \]