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How Do You Solve Two Equations with Two Variables?

Solve for a and b given:
a = 23 - 2b
3a + 3b = 48

Summary

  1. 'a' and 'b' are variables
  2. Plug (23-2b) in for 'a' in the second equation
  3. Distribute the 3, and combine the 'b' terms together
  4. Solve for 'b' by subtracting 69 from both sides and divide by -3
  5. b=7 and a=9
  6. Plug 7 in for 'b' to find 'a'
  7. Check our answers by plugging them into the second equation

Notes

    1. 'a' is a variable
    1. The second equation is '3a+3b=48'
    1. 'a' and 'b' are variables
    2. The right hand side of the first equation is: 23-2b
    3. This is equal to 'a'
    1. 'b' is a variable
    2. To distribute the 3, multiply it by 23 and then -2b
    1. To distribute the 3, multiply it by 23
    2. 3 times 23 is 69
    1. 'b' is a variable
    2. To distribute the 3, multiply it by 23 and then -2b
    3. 3 times -2b is -6b
    1. 'b' is a variable
    1. 'b' is a variable
    2. Negative 6b plus 3b is equal to negative 3b
    1. The positive and negative 69 cancel on the left hand side
    1. The positive and negative 69 cancel on the left hand side
    2. 48 minus 69 is negative 21
    1. The -3's cancel each other out on the left hand side
    2. -21 divided by -3 is equal to 7
    1. 'a' is a variable
    1. 'b' is a variable
    2. Anywhere you see a 'b' put a 7
    1. 2 • 7 = 14
    1. 23 - 14 = ?
    1. 23 - 14 = 9
    1. 3 • 9 = ?
    2. 3 • 7 = ?
    1. 3 • 9 = 27
    2. 3 • 7 = ?
    1. 3 • 9 = 27
    2. 3 • 7 = 21
    1. 27 + 21 = 48
    1. Plugging 7 in for 'b' and 9 in for 'a' into the second equation came out with a true statement: 48 = 48
    2. This means that our answers are correct!