Question

Use graphical method to solve the system of linear equations : $y = -3$ and $x + 2y = 4$.

Hint:

To find the intersection coordinate quickly without guessing, substitute $y = -3$ directly into the second equation:
\[ x + 2(-3) = 4 \implies x - 6 = 4 \implies x = 10 \]
Plot this specific point $(10, -3)$ to guarantee your graph is perfectly accurate!

Answer 1

Step 1: Solve algebraically first to know exactly where the lines should meet.
Substitute $y = -3$ directly into $x + 2y = 4$: $x + 2(-3) = 4 \implies x - 6 = 4 \implies x = 10$. So the lines must cross at $(10, -3)$.
Step 2: Choose easy plotting points for each line.
For $y = -3$, any point with $y$-coordinate $-3$ works, such as $(0,-3)$ and $(10,-3)$; this is a horizontal line. For $x + 2y = 4$, the intercepts are simple to use: at $y=0$, $x=4$, giving $(4,0)$; at $x=0$, $y=2$, giving $(0,2)$.
Step 3: Draw both lines on the same axes.
Plot the horizontal line through $(0,-3)$ and $(10,-3)$, and the line through $(4,0)$ and $(0,2)$, extending both far enough to see where they cross.
Step 4: Read off the intersection, which matches our algebraic check.
The two lines meet exactly at the point found in Step 1.
\[ \boxed{x = 10, \ y = -3} \]