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$2x+4y=6x-y$ ordered pairs

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Solve equations involving like terms

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Q.

2x+4y=6x-y

ordered pairs

Isolate Variables: Isolate the variables on one side of the equation to simplify it. $\newline$ We can start by moving all terms involving $x$ to one side and all terms involving $y$ to the other side. We do this by subtracting $2x$ from both sides and adding $y$ to both sides of the equation. $\newline$ $2x + 4y - 2x + y = 6x - y - 2x + y$ $\newline$ This simplifies to: $\newline$ $4y + y = 6x - 2x$
Combine Like Terms: Combine like terms. $\newline$ On the left side of the equation, we combine the $y$ terms, and on the right side, we combine the $x$ terms. $\newline$ $4y + y = 5y$ $\newline$ $6x - 2x = 4x$ $\newline$ So the equation now is: $\newline$ $5y = 4x$
Solve for y: Solve for y in terms of x. $\newline$ To solve for y, we need to divide both sides of the equation by $5$ . $\newline$ $\frac{5y}{5} = \frac{4x}{5}$ $\newline$ $y = \left(\frac{4}{5}\right)x$
Express as Ordered Pairs: Express the solution as ordered pairs. $\newline$ The equation $y = \frac{4}{5}x$ represents a linear relationship between $x$ and $y$ . To find ordered pairs that satisfy the equation, we can choose values for $x$ and calculate the corresponding $y$ values. $\newline$ For example, if $x = 0$ , then $y = \frac{4}{5}(0) = 0$ , so $(0, 0)$ is an ordered pair. $\newline$ If $x = 5$ , then $y = \frac{4}{5}(5) = 4$ , so $x$ $0$ is an ordered pair. $\newline$ We can continue to choose values for $x$ and calculate $y$ to get more ordered pairs.

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