Question:
Show through graphical method that the linear equation system \( 3x - y = 2 \) and \( 9x - 3y = 6 \) have infinite number of solutions.
Show through graphical method that the linear equation system \( 3x - y = 2 \) and \( 9x - 3y = 6 \) have infinite number of solutions.
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When two linear equations represent the same line, they have an infinite number of solutions.
Updated On: Oct 10, 2025
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Solution and Explanation
We are given the system of equations:
\[
3x - y = 2 \quad \text{(1)}
\]
and
\[
9x - 3y = 6 \quad \text{(2)}.
\]
To solve graphically, let's first rewrite both equations in slope-intercept form (\( y = mx + c \)).
Step 1: Convert equation (1) into slope-intercept form:
\[
3x - y = 2 \quad \implies \quad y = 3x - 2.
\]
Step 2: Convert equation (2) into slope-intercept form:
\[
9x - 3y = 6 \quad \implies \quad 3y = 9x - 6 \quad \implies \quad y = 3x - 2.
\]
Step 3: Observe the equations.
Both equations are in the form \( y = 3x - 2 \), indicating that the two lines are identical and overlap. Since both lines represent the same equation, they have infinite points of intersection, meaning the system has infinite solutions.
Conclusion:
Thus, the system of equations has infinite solutions, as the lines coincide.
Conclusion:
Thus, the system of equations has infinite solutions, as the lines coincide.
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