The table below shows four systems of equations:

1 answer:

4 0

To determine which system of equations would have the same solution, we evaluate each system of equations.

System 1 4x − 5y = 2, 3x − y = 8
x = 38/11
y = 26/11

System 2 4x − 5y = 2, 3x − 2y = 1
x = 1/7
y = -2/7

System 3 4x − 5y = 2, 3x − 8y = 4
x = -4/17
y = -10/17

System 4 4x − 5y = 2, 10x − 9y = 4
x = 1/7
y = -2/7


Therefore, the correct answer is option 3. System 2 and system 4 are equal, because the second equation in system 4 is obtained by adding the first equation in system 2 to two times the second equation in system 2.

4x− 5y = 2 2( 3x − 2y = 1)
----------------------- 10x - 9y = 4

You might be interested in

34 X 19/38 reduced to lowest term

torisob [31]

19/38 = 1/2 (divided top and bottom by 19)

34 X 19/38

= 34 X 1/2

= 34/2

= 17/1

Answer

17/1 (or 17)

7 0

2 years ago

What simple interest rate is needed for $6,000 to earn $1,000 in 15 months

Mekhanik [1.2K]

let's recall that a year has 12 months, so 15 months is really 15/12 years.

$\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$1000\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{15}{12}\dotfill &\frac{5}{4} \end{cases}$

$\bf 1000=(6000)r\left( \cfrac{5}{4} \right)\implies 1000=7500r\implies \cfrac{1000}{7500}=r\implies \cfrac{2}{15}=r \\\\\\ \stackrel{\textit{converting that to a percentage}}{\cfrac{2}{15}\cdot 100 = r\implies \cfrac{40}{3}=r}\implies \stackrel{\%~\hfill }{13.\overline{3}}=r$