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# $y = 3x - 5\;{\text{and}}\;6x = 2y + 10$ How do I solve this?

Last updated date: 20th Sep 2024
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Hint:First see if the lines are collinear lines or parallel lines or intersecting lines, two lines are said to be parallel if their ratios of coefficient of $x$ to coefficient of $y$ are equal, two lines are coincident if ratios of coefficient of $x$ to coefficient of $y$ are equal as well as the constant part too is equal and intersecting when ratios of coefficient of $x$ to coefficient of $y$ are not equal.
To solve the given equations $y = 3x - 5\;{\text{and}}\;6x = 2y + 10$,
If we see the equation of lines carefully, then we will find that the second equation is just multiplied with $2$ and has some balanced algebraic operation done which doesn’t affect the originality of the equation. We can see it as follows
$6x = 2y + 10 \\ \Rightarrow 6x - 10 = 2y \\ \Rightarrow 2 \times (3x - 5) = 2 \times y \\ \Rightarrow 3x - 5 = y \\ \Rightarrow y = 3x - 5 \\$