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{:[(1)/(3)x=9],[y-(1)/(3)x=2]:}
The system of equations above has solution (x,y). What is the value of y ?
(A) (9)/(2)
(B) (11)/(2)
(C) 7
(D) 11

$\begin{array}{c} \frac{1}{3} x=9 \\ y-\frac{1}{3} x=2 \end{array}$ $\newline$ The system of equations above has solution $(x, y)$ . What is the value of $y$ ? $\newline$ (A) $\frac{9}{2}$ $\newline$ (B) $\frac{11}{2}$ $\newline$ (C) $7$ $\newline$ (D) $11$

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Write an equation word problem

Full solution

Q.

\begin{array}{c} \frac{1}{3} x=9 \\ y-\frac{1}{3} x=2 \end{array}

\newline

The system of equations above has solution

(x, y)

. What is the value of

y

?

\newline

(A)

\frac{9}{2}

\newline

(B)

\frac{11}{2}

\newline

(C)

7

\newline

(D)

11

Solve for x: Solve the first equation for x. $\newline$ Given the equation $(\frac{1}{3})x = 9$ , we multiply both sides by $3$ to isolate x. $\newline$ $(\frac{1}{3})x \times 3 = 9 \times 3$ $\newline$ $x = 27$
Substitute into second equation: Substitute the value of $x$ into the second equation to solve for $y$ . We have $y - \frac{1}{3}x = 2$ and we know $x = 27$ , so we substitute $27$ for $x$ . $y - \frac{1}{3}(27) = 2$ $y - 9 = 2$
Add to solve for y: Add $9$ to both sides of the equation to solve for y. $\newline$ $y - 9 + 9 = 2 + 9$ $\newline$ $y = 11$

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