SAT Question 9f6f96ff: Systems of Linear Equations answer and explanation with Desmos solution

Choice D is correct. It's given that a wire with a length of $106$ inches is cut into two parts. It's also given that one part has a length of $x$ inches and the other part has a length of $y$ inches. This can be represented by the equation $x+y=106$. It's also given that the value of $x$ is $6$ more than $4$ times the value of $y$. This can be represented by the equation $x=4y+6$. Substituting $4y+6$ for $x$ in the equation $x+y=106$ yields $4y+6+y=106$, or $5y+6=106$. Subtracting $6$ from each side of this equation yields $5y=100$. Dividing each side of this equation by $5$ yields $y=20$. Substituting $20$ for $y$ in the equation $x=4y+6$ yields $x=4(20)+6$, or $x=86$.