Question

solve the system by graphing.\

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

select one:\
\bigcirc a. no solution.\
\bigcirc b. (2,2)\
\bigcirc c. (0,2)\
\bigcirc d. infinite solutions.

Explanation:

Step1: Set equations equal

Since $y=y$, equate the two expressions:
$$\frac{2}{3}x + 2 = -\frac{2}{3}x + 2$$

Step2: Isolate x terms

Subtract 2 from both sides, then add $\frac{2}{3}x$ to both sides:
$$\frac{2}{3}x + \frac{2}{3}x = 2 - 2$$
$$\frac{4}{3}x = 0$$

Step3: Solve for x

Multiply both sides by $\frac{3}{4}$:
$$x = 0 \times \frac{3}{4} = 0$$

Step4: Find y value

Substitute $x=0$ into $y=\frac{2}{3}x+2$:
$$y = \frac{2}{3}(0) + 2 = 2$$

Answer:

C. (0,2)