What is the solution to the system of equations 2x + y = 7 and y = 2x + 3?

by

To solve the system of equations:

  1. First, we have the two equations:
    • Equation 1: 2x + y = 7
    • Equation 2: y = 2x + 3
  2. We can substitute Equation 2 into Equation 1. Replace y in Equation 1 with 2x + 3:

    3. 2x + (2x + 3) = 7

  3. Simplifying this gives:

    4. 2x + 2x + 3 = 7

    4x + 3 = 7

  4. Now, subtract 3 from both sides:

    5. 4x = 4

  5. Next, divide each side by 4:

    6. x = 1

  6. Now that we have x, we can find y by substituting back into Equation 2:

    7. y = 2(1) + 3

    y = 2 + 3

    y = 5

  7. So, the solution to the system of equations is:

    8. (x, y) = (1, 5)

This means that the two equations intersect at the point (1, 5) on the coordinate plane.

Leave a Comment