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{:[y=(4)/(7)x],[(2)/(3)x=y+(5)/(7)]:}
Consider the system of equations. If
(x,y) is the solution to the system, then what is the value of
y ?
Choose 1 answer:
(A)
(2)/(21)
(B)
(30)/(7)
(c)
(15)/(2)
D None of the above

$\begin{array}{c} y=\frac{4}{7} x \\ \frac{2}{3} x=y+\frac{5}{7} \end{array}$ $\newline$ Consider the system of equations. If $(x, y)$ is the solution to the system, then what is the value of $y$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{2}{21}$ $\newline$ (B) $\frac{30}{7}$ $\newline$ (C) $\frac{15}{2}$ $\newline$ (D) None of the above

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Compare linear and exponential growth

Full solution

Q.

\begin{array}{c} y=\frac{4}{7} x \\ \frac{2}{3} x=y+\frac{5}{7} \end{array}

\newline

Consider the system of equations. If

(x, y)

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

y

?

\newline

Choose

1

answer:

\newline

(A)

\frac{2}{21}

\newline

(B)

\frac{30}{7}

\newline

(C)

\frac{15}{2}

\newline

(D) None of the above

Write down system of equations: First, let's write down the system of equations: $\newline$ $y = \frac{4}{7}x$ $\newline$ $\frac{2}{3}x = y + \frac{5}{7}$ $\newline$ We need to solve this system to find the value of $y$ .
Substitute expression for y: To solve the system, we can substitute the expression for y from the first equation into the second equation: $\newline$ $(\frac{2}{3})x = (\frac{4}{7})x + (\frac{5}{7})$ $\newline$ Now we have an equation with just one variable, $x$ , which we can solve.
Solve for x: Next, we'll solve for x. To do this, we need to get all the x terms on one side and the constants on the other side. We can start by multiplying both sides of the equation by $21$ (the least common multiple of $3$ and $7$ ) to clear the fractions: $\newline$ $21 \times \left(\frac{2}{3}\right)x = 21 \times \left(\frac{4}{7}\right)x + 21 \times \left(\frac{5}{7}\right)$ $\newline$ This simplifies to: $\newline$ $14x = 12x + 15$
Isolate x terms: Now, we subtract $12x$ from both sides to isolate the x terms: $\newline$ $14x - 12x = 15$ $\newline$ $2x = 15$ $\newline$ Next, we divide both sides by $2$ to solve for x: $\newline$ $x = \frac{15}{2}$
Divide both sides by $2$ : Now that we have the value of $x$ , we can substitute it back into the first equation to find $y$ : $\newline$ $y = \left(\frac{4}{7}\right)\left(\frac{15}{2}\right)$
Substitute $x$ back into first equation: We multiply the numbers to find $y$ :
$y = \frac{(4 \times 15)}{(7 \times 2)}$
$y = \frac{60}{14}$
$y = \frac{30}{7}$
Multiply to find $y$ : The value of $y$ is $\frac{$ $30$ }{ $7$ }, which corresponds to answer choice (math)(B).

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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\newline

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