Question

solving systems of linear equations: medium
google classroom microsoft teams
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 -\frac{1}{8}
b \frac{1}{8}
c 1
d there are no solutions to this system of equations.

Explanation:

Step1: Simplify the first equation

Starting with $3z - 4y=2z - 4.5$, we can subtract $2z$ from both sides to get $z-4y=- 4.5$, which can be rewritten as $z = 4y - 4.5$.

Step2: Substitute $z$ into the second - equation

The second equation is $8y=2z + 5$. Substitute $z = 4y - 4.5$ into it:
\[

$$\begin{align*} 8y&=2(4y - 4.5)+5\\ 8y&=8y-9 + 5\\ 8y&=8y - 4 \end{align*}$$

\]
This equation $8y=8y - 4$ simplifies to $0=-4$, which is a contradiction.

Answer:

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