Leonard and liam each own a collection of vintage cars. leonard has 7 cars more than liam has. three times the number of cars leonard has and two times the number of cars liam has add up to 96. the system of linear equations that relates the number of cars leonard has (x) and the number of cars liam has (y) is . the solution of this system is .

 The system of equations  

x = y + 7

3x + 2y = 96  

Solution:   22, 15

Step-by-step explanation:

Set up the facts (use  "=" in place of verbs like "has" or "is") Leonard x, Liam y.

x = y + 7   and 3x + 2y = 96.

There is a nice value for (x) that you can substitute: x = y + 7.   So use that value to rewrite the second equation:

3(y+7) + 2y = 96   Distribute and add like terms

3y + 21 + 2y = 96    becomes 5y + 21 = 96  subtract 21 from both sides

5y = 96 - 21  becomes  5y = 75.  Divide both sides by 5.

y = 15.   Substitute 15 in place of y in the first equation and solve for x.

x = 15 + 7  So x = 22

Leonard has 22 cars, Liam has 15.

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