How can we solve the system of linear equations: y = x + 6 and y = x + 10?

by

Solution to the System of Linear Equations

To solve the system of equations:

  1. Equation 1: y = x + 6
  2. Equation 2: y = x + 10

We start by setting the two equations for y equal to each other since both represent y:

x + 6 = x + 10

Next, we can simplify this equation:

  • Subtract x from both sides:
    • 6 = 10
  • This shows that the two equations do not intersect, as 6 does not equal 10.

Conclusion

Since we arrived at a contradiction (6 = 10), this system of equations has no solution. This means that the lines represented by these equations are parallel and will never intersect.

Leave a Comment