Solve graphically each of the following systems of linear equations. Also, find the coordinates of the points where the lines meet the axis of y.
`x + 2y -7=0`
`2x -y-4 =0`

Answer

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

### Step 1: Write the equations in slope-intercept form
The given equations are:
1. \( x + 2y - 7 = 0 \)
2. \( 2x - y - 4 = 0 \)

We will rearrange both equations to express \( y \) in terms of \( x \).

**For the first equation:**
\[ x + 2y - 7 = 0 \implies 2y = 7 - x \implies y = \frac{7 - x}{2} \implies y = \frac{7}{2} - \frac{1}{2}x \]

**For the second equation:**
\[ 2x - y - 4 = 0 \implies y = 2x - 4 \]

### Step 2: Find the intercepts
To find where each line meets the y-axis, we set \( x = 0 \).

**For the first equation:**
\[ y = \frac{7}{2} - \frac{1}{2}(0) = \frac{7}{2} \implies (0, \frac{7}{2}) \text{ or } (0, 3.5) \]

**For the second equation:**
\[ y = 2(0) - 4 = -4 \implies (0, -4) \]

### Step 3: Find another point for each line
To graph the lines, we need at least two points for each line.

**For the first equation \( y = \frac{7}{2} - \frac{1}{2}x \):**
- Let \( x = 2 \):
\[ y = \frac{7}{2} - \frac{1}{2}(2) = \frac{7}{2} - 1 = \frac{5}{2} \implies (2, \frac{5}{2}) \text{ or } (2, 2.5) \]

**For the second equation \( y = 2x - 4 \):**
- Let \( x = 2 \):
\[ y = 2(2) - 4 = 4 - 4 = 0 \implies (2, 0) \]

### Step 4: Plot the points and draw the lines
Now we can plot the points:
1. For the first line: \( (0, 3.5) \) and \( (2, 2.5) \)
2. For the second line: \( (0, -4) \) and \( (2, 0) \)

Draw the lines through these points.

### Step 5: Find the intersection point
To find the coordinates where the two lines intersect, we can solve the equations simultaneously.

From the first equation:
\[ x + 2y = 7 \quad (1) \]
From the second equation:
\[ 2x - y = 4 \quad (2) \]

We can multiply equation (2) by 2:
\[ 4x - 2y = 8 \quad (3) \]

Now, we can add equations (1) and (3):
\[ x + 2y + 4x - 2y = 7 + 8 \implies 5x = 15 \implies x = 3 \]

Substituting \( x = 3 \) back into equation (1):
\[ 3 + 2y = 7 \implies 2y = 4 \implies y = 2 \]

Thus, the intersection point is \( (3, 2) \).

### Summary of Results
- The lines meet the y-axis at:
- For \( x + 2y - 7 = 0 \): \( (0, 3.5) \)
- For \( 2x - y - 4 = 0 \): \( (0, -4) \)
- The intersection point of the two lines is \( (3, 2) \).