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3x-4y=10

2x-4y=6
If
(x,y) satisfies the given system of equations, what is the value of
y ?
Choose 1 answer:
(A)
(1)/(10)
(B)
(1)/(2)
(c)
(16)/(5)
(D) 4

$\begin{array}{l} 3 x-4 y=10 \\ 2 x-4 y=6 \end{array}$ $\newline$ If $(x, y)$ satisfies the given system of equations, what is the value of $y$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{10}$ $\newline$ (B) $\frac{1}{2}$ $\newline$ (C) $\frac{16}{5}$ $\newline$ (D) $4$

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Domain and range

Full solution

Q.

\begin{array}{l} 3 x-4 y=10 \\ 2 x-4 y=6 \end{array}

\newline

If

(x, y)

satisfies the given system of equations, what is the value of

y

?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{10}

\newline

(B)

\frac{1}{2}

\newline

(C)

\frac{16}{5}

\newline

(D)

4

Equations: We have the system of equations: $\newline$ $3x - 4y = 10$ ( $1$ ) $\newline$ $2x - 4y = 6$ ( $2$ ) $\newline$ To find the value of $y$ , we can subtract equation ( $2$ ) from equation ( $1$ ) to eliminate $y$ .
Eliminating y: Subtracting equation ( $2$ ) from equation ( $1$ ) gives us: $\newline$ $(3x - 4y) - (2x - 4y) = 10 - 6$ $\newline$ This simplifies to: $\newline$ $3x - 2x = 10 - 6$
Simplifying equation: Simplifying the above equation gives us: $\newline$ $x = 4$ $\newline$ Now we have the value of $x$ .
Finding x: Next, we substitute the value of $x$ back into one of the original equations to solve for $y$ . We can use equation ( $2$ ) for this purpose: $\newline$ $2x - 4y = 6$ $\newline$ Substituting $x = 4$ gives us: $\newline$ $2(4) - 4y = 6$
Substituting $x$ into equation: Solving the above equation for $y$ gives us: $\newline$ $8 - 4y = 6$ $\newline$ Subtracting $8$ from both sides gives us: $\newline$ $-4y = 6 - 8$
Solving for y: Simplifying the above equation gives us: $\newline$ $-4y = -2$ $\newline$ Dividing both sides by $-4$ gives us: $\newline$ $y = \frac{-2}{-4}$
Final value of y: Solving the above equation for y gives us: $\newline$ y = $\frac{1}{2}$ $\newline$ So the value of y is $\frac{1}{2}$ , which corresponds to choice (B).

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\newline

\newline

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\newline

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\newline

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\newline

\newline

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\newline

\newline

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\newline

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\newline

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