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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 .

Respuesta :

In order to find the solution of the system we need to solve:
x = y+7
3x+2y=96

where x = number of cars that Leonard has
and y = number of Liam's cars

3(y+7)+27=96
3y+21+27=96
3y+48=96
3y=48
y=16
x=16+7=23

Answer: The answer is (22, 15).

Step-by-step explanation:  Given that 'x' represents the number of cars Leonard has and 'y' represents the number of cars Liam has.

Then, according to the given information, we have

[tex]x-y=7,\\\\3x+2y=96.[/tex]

Multiplying the first equation by 2 and adding to the second equation, we have

[tex]2x+3x=14+96\\\\\Rightarrow 5x=110\\\\\Rightarrow x=22.[/tex]

So,

[tex]y=x-7=22-7=15.[/tex]

Therefore, Leonard has 22 cars and Liam has 15 cars.

Thus, (22, 15) is the solution to the given system.

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