Solve the pair of linear equations graphically.

• 2x + y - 6 = 0
• 4x - 2y - 4 = 0

To solve the pair of linear equations graphically, we first need to rewrite each equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Step 1: Rearranging the Equations

For the first equation, 2x + y - 6 = 0:

• Rearranging gives: y = -2x + 6

For the second equation, 4x - 2y - 4 = 0:

• Rearranging gives: -2y = -4x + 4
• Dividing by -2 results in: y = 2x - 2

Step 2: Plotting the Equations

Now, we can plot both equations on a graph:

Equation 1: y = -2x + 6

• Y-intercept (0, 6)
• Another point: When x = 3, y = 0 (point (3, 0))

Equation 2: y = 2x - 2

• Y-intercept (0, -2)
• Another point: When x = 2, y = 2 (point (2, 2))

Step 3: Finding the Intersection

After plotting both lines on the same graph, look for the point where they intersect. This point represents the solution to the system of equations.

Result

The lines intersect at the point (2, 2). Therefore, the solution to the pair of linear equations is:

• x = 2
• y = 2