SAT Question 0c541d87: Systems of Linear Equations answer and explanation with Desmos solution

Choice D is correct. Let $l$ represent the cost, in dollars, of $1$ loaf of bread, and let $d$ represent the cost, in dollars, of $1$ dozen eggs. It's given that the first customer paid $12.45$ dollars for $1$ loaf of bread and $2$ dozen eggs. Therefore, the first customer's purchase can be represented by the equation $l+2d=12.45$. It's also given that the second customer paid $19.42$ dollars for $4$ loaves of bread and $1$ dozen eggs. Therefore, the second customer's purchase can be represented by the equation $4l+d=19.42$. The equations $l+2d=12.45$ and $4l+d=19.42$ form a system of linear equations, which can be solved by elimination to find the value of $d$. Multiplying the first equation in the system by $-4$ yields $-4l-8d=-49.8$. Adding $-4l-8d=-49.8$ to the second equation, $4l+d=19.42$, yields $\left(-4l+4l\right)+\left(-8d+d\right)=\left(-49.8+19.42\right)$, which is equivalent to $-7d=-30.38$. Dividing both sides of this equation by $-7$ yields $d=4.34$. Therefore, the cost, in dollars, of $1$ dozen eggs is $4.34$.