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Lesson 2: Solving Systems of Linear Equations in Two Variables by Substitution Let's Do More: Find the Hive Two bees each found a food source. The first bee's path back to the hive follows the line y = 2x + 7. The second bees path follows the line 4x + y = 31. Their path cross at the hive. Find the coordinate of the hive. Solve this problem by Substitution.​

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Problem:

Find the Hive Two bees each found a food source. The first bee's path back to the hive follows the line y = 2x + 7. The second bees path follows the line 4x + y = 31. Their path cross at the hive. Find the coordinate of the hive. Solve this problem by Substitution.

Solution:

Solve the systems of linear equation in two variables by substitution method.

  • y = 2x + 7 and 4x + y = 31

Substitute the expression for y into the second equation. Then, solve the equation.

  • 4x + y = 31
  • 4x + (2x + 7) = 31
  • 6x + 7 = 31
  • 6x = 31 - 7
  • 6x = 24/6
  • x = 4

Substitute the value into the value of x to the equation and solve.

  • y = 2x + 7
  • y = 2(4) + 7
  • y = 8 + 7
  • y = 15

Checking:

Check the values of the variables obtained by substituting to the linear equations in the system.

  • x = 4 and y = 15

Equation 1:

  • y = 2x + 7
  • (15) = 2(4) + 7
  • 15 = 8 + 7
  • 15 = 15 ✔

Equation 2:

  • 4x + y = 31
  • 4(4) + (15) = 31
  • 16 + 15 = 31
  • 31 = 31 ✔

Answer:

∴ Therefore, the solution of set is {4, 15}.

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