Question

select the correct answer from each drop-down menu.
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
.
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Explanation:

Step1: Define equations from text

1. $x = y +7$
2. $3x + 2y =96$

Step2: Substitute $x$ into second equation

$3(y+7) +2y =96$
$3y +21 +2y =96$
$5y = 96-21 =75$

Step3: Solve for $y$

$y = \frac{75}{5}=15$

Step4: Solve for $x$

$x =15 +7 =22$

Answer:

1. The system of equations is $\boldsymbol{x=y+7}$ and $\boldsymbol{3x+2y=96}$
2. The solution is $x=22$, $y=15$ (Leonard has 22 cars, Liam has 15 cars)