Question

(b) problem 16: (first taught in lesson 29) $\triangle abc$ is equilateral and $ab = 4x - y$, $bc = 2x + 3y$, and $ac = 7$. find $x$ and $y$. after you enter your answer press go. $x = $ $y = $

Explanation:

Step1: Set up equations

Since $\triangle ABC$ is equilateral, $AB = BC=AC$. So we have the system of equations:

$$\begin{cases}4x - y=7\\2x + 3y=7\end{cases}$$

Step2: Multiply the second - equation

Multiply the second equation $2x + 3y=7$ by $2$ to get $4x+6y = 14$.

Step3: Subtract equations

Subtract the first equation $4x - y=7$ from $4x+6y = 14$:
$(4x + 6y)-(4x - y)=14 - 7$
$4x+6y - 4x + y=7$
$7y=7$, so $y = 1$.

Step4: Find the value of $x$

Substitute $y = 1$ into the first equation $4x - y=7$, we get $4x-1 = 7$.
$4x=7 + 1=8$, then $x = 2$.

Answer:

$x = 2$, $y = 1$