Question

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 .

Answer 1

Answer: The system of equations

x = y + 7

3x + 2y = 96

Solution: 22, 15

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.

Answer 2

The system of equations according to the given information is the following:
x=7+y
3x+2y=96

There are multiple ways to solve this, but using addition is probably the fastest. Rearrange the equations into corresponding formats like this:
x-y=7
3x+2y=96

Then match the coefficients of one of the variables:
2x-2y=14
3x+2y=96

Then add the two equations together to find x:

5x=110
x=22 cars

So Leonard has 22 cars, and since he has seven more cars than Liam, Liam has 15 cars.