Question

find the solution to the system of equations. you can use the interactive graph below to find the solution. \\(\

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

\\) \\(x = \square\\) \\(y = \square\\) graph omitted

Explanation:

Step1: Set equations equal

Since $y=y$, equate the two expressions:
$2x + 3 = -3x + 3$

Step2: Solve for $x$

Isolate $x$ terms, simplify:
$2x + 3x = 3 - 3$
$5x = 0$
$x = \frac{0}{5} = 0$

Step3: Find $y$ via substitution

Substitute $x=0$ into $y=2x+3$:
$y = 2(0) + 3 = 3$

Answer:

$x = 0$
$y = 3$