Question

Draw the graph of the pair of linear equations \( 3x - 5y + 1 = 0 \) and \( 2x - y + 3 = 0 \) and solve them.

Hint:

For graphical solutions, convert equations to \( y = mx + c \) form and plot the intercepts.

Answer 1

To solve this system graphically, we find the coordinates where these two lines intersect.
Step 1: Expressing in Slope-Intercept Form Rearrange both equations:
\[ y = \frac{3}{5}x + \frac{1}{5} \] \[ y = 2x + 3 \] Step 2: Finding Intercepts
For \( 3x - 5y + 1 = 0 \):
- When \( x = 0 \), \( y = -\frac{1}{5} \).
- When \( y = 0 \), \( x = -\frac{1}{3} \).
For \( 2x - y + 3 = 0 \):
- When \( x = 0 \), \( y = -3 \).
- When \( y = 0 \), \( x = \frac{3}{2} \).
Step 3: Plotting and Finding Intersection Plot these points on a graph, and the intersection point gives the solution.