Question3. Graph the system of equations on the coordinate plane. $$\begin{array}{l} 2 x+3 y=-9 \\ y=4 x+1 \end{array}$$

Studdy Solution
Determine the intersection point of the two lines.
- Solve the system of equations to find the intersection point. - Set the equations equal to each other:
$$-\frac{2}{3}x - 3 = 4x + 1$$
$$-\frac{2}{3}x - 4x = 1 + 3$$
$$-\frac{14}{3}x = 4$$
$$x = -\frac{12}{14} = -\frac{6}{7}$$
Substitute $x = -\frac{6}{7}$ into $y = 4x + 1$:
$$y = 4\left(-\frac{6}{7}\right) + 1$$
$$y = -\frac{24}{7} + 1$$
$$y = -\frac{24}{7} + \frac{7}{7}$$
$$y = -\frac{17}{7}$$
The intersection point is $\left(-\frac{6}{7}, -\frac{17}{7}\right)$.