Question

2 \\(\

$$\begin{cases} y = 2x - 6 \\\\ y = -3x + 4 \\end{cases}$$

\\)
solution: ________

Explanation:

Step1: Set equations equal

Since $y = 2x - 6$ and $y = -3x + 4$, set $2x - 6 = -3x + 4$.

Step2: Solve for x

Add $3x$ to both sides: $2x + 3x - 6 = 4$ → $5x - 6 = 4$.
Add 6 to both sides: $5x = 4 + 6$ → $5x = 10$.
Divide by 5: $x = \frac{10}{5} = 2$.

Step3: Find y with x=2

Substitute $x=2$ into $y=2x-6$: $y = 2(2) - 6 = 4 - 6 = -2$.

Step4: Verify with second equation

Substitute $x=2$ into $y=-3x+4$: $y = -3(2) + 4 = -6 + 4 = -2$.

Answer:

$(2, -2)$