Question

Use graphical method to solve the system of linear equations : $x = -3$ and $5x - 2y = -5$.

Hint:

To find the intersection coordinate quickly without guessing, substitute $x = -3$ directly into the second equation:
\[ 5(-3) - 2y = -5 \implies -15 - 2y = -5 \implies 2y = -10 \implies y = -5 \]
Plot this specific point $(-3, -5)$ to guarantee your graph is perfectly accurate!

Answer 1

Step 1: Find the intersection point algebraically first, then use it to guide the graph.
Since one line is simply $x=-3$, substitute this value straight into the second equation instead of tabulating extra points.
Step 2: Substitute $x=-3$ into $5x-2y=-5$.
\[ 5(-3) - 2y = -5 \implies -15-2y=-5 \implies -2y = 10 \implies y=-5 \]
Step 3: Plot both lines using this guaranteed point plus one more each.
Line $x=-3$ is the vertical line through $(-3,0)$ and $(-3,-5)$. For $5x-2y=-5$, another convenient point is where $x=-1$, giving $y=0$, i.e. $(-1,0)$. Draw both lines through these points.
Step 4: Read off the intersection.
Both lines meet exactly at $(-3,-5)$, which is the solution, matching what we calculated algebraically.
\[ \boxed{x=-3,\ y=-5} \]