Solve graphically : 2x +y=8, x-y=1

Answer

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

### Step 1: Write the equations in slope-intercept form
The given equations are:
1. \(2x + y = 8\)
2. \(x - y = 1\)

We will convert these equations to the form \(y = mx + b\).

**For the first equation:**
\[ y = 8 - 2x \]

**For the second equation:**
\[ y = x - 1 \]

### Step 2: Create a table of values for each equation
We will choose some values for \(x\) and calculate the corresponding \(y\) values.

**For the first equation \(y = 8 - 2x\):**
- If \(x = 0\), \(y = 8 - 2(0) = 8\) → Point (0, 8)
- If \(x = 1\), \(y = 8 - 2(1) = 6\) → Point (1, 6)
- If \(x = 2\), \(y = 8 - 2(2) = 4\) → Point (2, 4)
- If \(x = 3\), \(y = 8 - 2(3) = 2\) → Point (3, 2)
- If \(x = 4\), \(y = 8 - 2(4) = 0\) → Point (4, 0)

**For the second equation \(y = x - 1\):**
- If \(x = 0\), \(y = 0 - 1 = -1\) → Point (0, -1)
- If \(x = 1\), \(y = 1 - 1 = 0\) → Point (1, 0)
- If \(x = 2\), \(y = 2 - 1 = 1\) → Point (2, 1)
- If \(x = 3\), \(y = 3 - 1 = 2\) → Point (3, 2)
- If \(x = 4\), \(y = 4 - 1 = 3\) → Point (4, 3)

### Step 3: Plot the points on a graph
- For the first equation, plot the points (0, 8), (1, 6), (2, 4), (3, 2), and (4, 0).
- For the second equation, plot the points (0, -1), (1, 0), (2, 1), (3, 2), and (4, 3).

### Step 4: Draw the lines
- Draw a straight line through the points plotted for the first equation.
- Draw another straight line through the points plotted for the second equation.

### Step 5: Find the intersection point
The intersection point of the two lines is the solution to the system of equations. From the graph, we can see that the lines intersect at the point (3, 2).

### Final Solution
Thus, the solution to the equations \(2x + y = 8\) and \(x - y = 1\) is:
\[ (x, y) = (3, 2) \]

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