Question

Plzzzz help don’t understand this question plz explain

Answer 1

7d + 2s = 45, 14d + 11s = 174

Solve for d in the first equation.

7d = 45 - 2s

d = 45/7 - 2/7s

Substitute d into the second equation.

14(45/7 - 2/7s) + 11s = 174

90 - 4s + 11s = 174

90 + 7s = 174

7s = 84

s = 12

Substitute s into the first equation.

7d + 2(12) = 45

7d + 24 = 45

7d = 21

d = 3

s = 12, d = 3

Answer 2

This exercise wants you to build a linear system of two equations and two unknowns.

To do so, we assign a variable to each of the quantity we want to calculate, so let's call $d$ the cost of one daylily and $s$ the cost of one shrub.

We know that Ashley bought 7 daylilies and 2 shrubs, so she paid

$7d+2s = 45$

Similarly, Lisa spent

$14d+11s = 174$

for 14 daylilies and 11 shrubs.

So, the system is

$\begin{cases} 7d+2s = 45\\ 14d+11s = 174 \end{cases}$

To solve the system, we must manipulate its equations in order to find the value of one particular variables. For example, we can multiply the first equation by 2 to get

$\begin{cases}14d+4s = 90\\14d+11s = 174\end{cases}$

Now, if you subtract the first equation from the second you have

$7s = 84 \implies s = 12$

So, one shrub costs 12 dollars. We can substitute this value for $s$ in any of the equation, and solve it for $d$. For example, if we choose the first one we have

$7d+2s = 7d+24= 45 \implies 7d = 21 \implies d=3$

So, one daylily costs 3 dollars.