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3z-4y=2z-4.5

8y=2z+5
Consider the system of equations. If
(y,z) is the solution to the system, then what is the value of
y-z ?
Choose 1 answer:
(A)
-(1)/(8)
(B)
(1)/(8)
(c) 1
(D) There are no solutions to this system of equations.

$3 z-4 y=2 z-4.5$ $\newline$ $8 y=2 z+5$ $\newline$ Consider the system of equations. If $(y, z)$ is the solution to the system, then what is the value of $y-z$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{1}{8}$ $\newline$ (B) $\frac{1}{8}$ $\newline$ (C) $1$ $\newline$ (D) There are no solutions to this system of equations.

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Solve rational equations

Full solution

Q.

3 z-4 y=2 z-4.5

\newline

8 y=2 z+5

\newline

Consider the system of equations. If

(y, z)

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

y-z

?

\newline

Choose

1

answer:

\newline

(A)

-\frac{1}{8}

\newline

(B)

\frac{1}{8}

\newline

(C)

1

\newline

(D) There are no solutions to this system of equations.

Simplify first equation: We are given the system of equations: $\newline$ $1$ ) $3z - 4y = 2z - 4.5$ $\newline$ $2$ ) $8y = 2z + 5$ $\newline$ We need to find the value of $y - z$ . Let's start by simplifying the first equation to isolate $z$ . $\newline$ Subtract $2z$ from both sides of the first equation: $\newline$ $3z - 4y - 2z = 2z - 4.5 - 2z$ $\newline$ This simplifies to: $\newline$ $z - 4y = -4.5$
Express $y$ in terms of $z$ : Now, let's express $y$ in terms of $z$ using the second equation. $\newline$ Divide both sides of the second equation by $8$ : $\newline$ $\frac{8y}{8} = \frac{2z + 5}{8}$ $\newline$ This simplifies to: $\newline$ $y = \frac{2z + 5}{8}$
Substitute $y$ into first equation: Substitute the expression for $y$ from Step $2$ into the simplified first equation from Step $1$ : $\newline$ $z - 4((2z + 5) / 8) = -4.5$ $\newline$ Multiply both sides of the equation by $8$ to eliminate the fraction: $\newline$ $8z - 4(2z + 5) = -4.5 \times 8$ $\newline$ This simplifies to: $\newline$ $8z - 8z - 20 = -36$

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