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y=(1)/(3)x+5
y=2x
Consider the given system of equations. If (x,y) is the solution to the system, then what is the value of
y+x ?

◻

$y = \frac{1}{3}x+5$ $\newline$ $y= 2x$ $\newline$ Consider the given system of equations. If $(x,y)$ is the solution to the system, then what is the value of $\newline$ $y+x$ ? $\newline$ ◻

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Write and solve direct variation equations

Full solution

Q.

y = \frac{1}{3}x+5

\newline

y= 2x

\newline

Consider the given system of equations. If

(x,y)

is the solution to the system, then what is the value of

\newline

y+x

?

\newline

◻

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $y = \frac{1}{3}x + 5$ $\newline$ $y = 2x$
Set Equal: Set the two equations equal to each other to find the value of $x$ . $\newline$ Since both expressions are equal to $y$ , we can set them equal to each other: $\newline$ $\frac{1}{3}x + 5 = 2x$
Solve for x: Solve for x. $\newline$ To find $x$ , we need to get all the $x$ terms on one side and the constants on the other side. We can do this by subtracting $(1/3)x$ from both sides: $\newline$ $(1/3)x + 5 - (1/3)x = 2x - (1/3)x$ $\newline$ $5 = (6/3)x - (1/3)x$ $\newline$ $5 = (5/3)x$ $\newline$ Now, multiply both sides by the reciprocal of $(5/3)$ to solve for $x$ : $\newline$ $5 * (3/5) = x$ $\newline$ $3 = x$
Substitute and Find $y$ : Substitute the value of $x$ into one of the original equations to find $y$ . We can use either equation, but for simplicity, let's use $y = 2x$ : $y = 2(3)$ $y = 6$
Find $y + x$ : Add the values of $x$ and $y$ to find $y + x$ . $\newline$ $y + x = 6 + 3$ $\newline$ $y + x = 9$

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