Answer:
Cost of one rose bush = $2 and cost of 1 geranium = $11
Step-by-step explanation:
lets assume cost of one rose bush = $x
lets assume cost of one geranium = $y
Given that Norachai spent $13 on 1 rose and 1 geranium
⇒ 1 × (cost of one rose bush) + 1× (cost of one geranium) = 13
⇒ 1x + 1y = 13 ----------------------------equation 1
Also given that Castel spent $46 on 1 rose bush and 4 geraniums
⇒1 × (cost of one rose bush) + 4× (cost of one geranium) = 46
⇒ 1x + 4y = 46 ----------------------------equation 2
Now we are having following two equations which will be used to find the value of x and y
1x + 1y = 13 ----------------------------equation 1
1x + 4y = 46 ----------------------------equation 2
lets modify equation 1 to get value of y in terms of x and name that equation as equation 3
1x + 1y = 13 ----------------------------equation 1
⇒ y = 13 - x -----------------------------equation 3
On substituting value of y from equation 3 in equation 2 we get
1x + 4 × ( 13 - x ) = 46
⇒ x + 52-4x =46
⇒ -3x = 46-52
⇒ x = (-6)/(-3) = 2
on substituting calculated value of x that is 2 in equation 3 we get
y = 13 -2 = 11
so on solving the equations we get x = 2 and y = 11.
Hence cost of 1 rose bush = $x = $2 and cost of 1 geranium = $y = $11
