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8x-y=12
2x-6y=3
Consider the system of equations. If (x,y) is the solution to the system, then what is the value of x+y?
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$8x-y=12$ $\newline$ $2x-6y=3$ $\newline$ Consider the system of equations. If $(x,y)$ is the solution to the system, then what is the value of $x+y$ ? $\newline$ $\square$

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Write an equation word problem

Full solution

Q.

8x-y=12

\newline

2x-6y=3

\newline

Consider the system of equations. If

(x,y)

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

x+y

?

\newline

\square

Multiply by $4$ : First, let's multiply the second equation by $4$ to make the coefficients of $x$ the same in both equations. $\newline$ $4(2x - 6y) = 4\times 3$ $\newline$ $8x - 24y = 12$
Eliminate x: Now we have two equations with the same coefficient for x: $\newline$ $1$ ) $8x - y = 12$ $\newline$ $2$ ) $8x - 24y = 12$ $\newline$ Subtract the second equation from the first to eliminate x. $\newline$ $(8x - y) - (8x - 24y) = 12 - 12$ $\newline$ $-y + 24y = 0$ $\newline$ $23y = 0$
Solve for y: Divide both sides by $23$ to solve for $y$ . $\newline$ $y = \frac{0}{23}$ $\newline$ $y = 0$
Substitute into equation: Now that we have the value of $y$ , we can substitute it back into one of the original equations to find $x$ . Let's use the first equation: $8x - y = 12$ $8x - 0 = 12$ $8x = 12$
Solve for x: Divide both sides by $8$ to solve for x. $\newline$ $x = \frac{12}{8}$ $\newline$ $x = 1.5$

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